Transform-based image coding method and apparatus therefor

ABSTRACT

An image decoding method according to the present document comprises the steps of: deriving a transform coefficient for a current block on the basis of residual information; deriving a residual sample by applying, to the transform coefficient, at least one of LFNST and MTS; and generating a reconstructed picture on the basis of the residual samples, wherein the LFNST is performed on the basis of an LFNST index indicating an LFNST kernel, the MTS is performed on the basis of an MTS index indicating an MTS kernel, and the LFNST index may be parsed before the MTS index.

FIELD OF THE DISCLOSURE

The present disclosure relates to an image coding technique and, moreparticularly, to a method and an apparatus for coding an image based ontransform in an image coding system.

RELATED ART

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium, the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing efficiency in transform indexcoding.

Still another technical aspect of the present disclosure is to providean image coding method and apparatus using LFNST and MTS.

Still another technical aspect of the present disclosure is to providean image coding method and apparatus for LFNST index and MTS indexsignaling.

According to an embodiment of the present disclosure, an image decodingmethod performed by a decoding apparatus is provided. The method mayinclude deriving transform coefficients for a current block based on theresidual information; deriving residual samples by applying at least oneof LFNST and MTS to the transform coefficient; and generating areconstructed picture based on the residual samples, wherein the LFNSTmay be performed based on an LFNST index indicating an LFNST kernel,wherein the MTS may be performed based on an MTS index indicating an MTSkernel, and wherein the LFNST index may be parsed before the MTS index.

The residual information may include last significant coefficientposition information, and the LFNST index is parsed after the lastsignificant coefficient position information has been parsed.

When the current block is a luma block and the LFNST index is 0, the MTSindex may be parsed.

When the tree type of the current block is a dual tree, the LFNST indexfor each of the luma block and the chroma block may be parsed.

The deriving the transform coefficient may include deriving a width anda height for the top-left region in which the last significantcoefficient may exist in the current block by zero-out, and the widthand height for the top-left region may be derived before parsing the MTSindex.

The position of the last significant coefficient may be derived by thewidth and the height for the top-left region, and the last significantcoefficient position information may be binarized based on the width andthe height for the top-left region.

According to an embodiment of the present disclosure, an image encodingmethod performed by an encoding apparatus is provided. The method mayinclude deriving transform coefficients by applying at least one ofLFNST and MTS for the residual samples; and encoding quantized residualinformation and at least one of an LFNST index indicating an LFNSTkernel and an MTS index indicating an MTS kernel, wherein the LFNSTindex may be signaled before the MTS index.

According to still another embodiment of the present disclosure, theremay be provided a digital storage medium that stores image dataincluding encoded image information and a bitstream generated accordingto an image encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, there maybe provided a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

According to the present disclosure, it is possible to increase overallimage/video compression efficiency.

According to the present disclosure, it is possible to increaseefficiency in transform index coding.

Still another technical aspect of the present disclosure provides animage coding method and apparatus using LFNST and MTS.

Still another technical aspect of the present disclosure can provide animage coding method and apparatus for LFNST index and MTS indexsignaling.

The effects that can be obtained through specific examples of thepresent disclosure are not limited to the effects listed above. Forexample, there may be various technical effects that a person havingordinary skill in the related art can understand or derive from thepresent disclosure. Accordingly, specific effects of the presentdisclosure are not limited to those explicitly described in the presentdisclosure and may include various effects that can be understood orderived from the technical features of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram schematically describing a configuration of avideo/image encoding apparatus to which the present document may beapplied.

FIG. 2 is a diagram schematically describing a configuration of avideo/image decoding apparatus to which the present document may beapplied.

FIG. 3 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

FIG. 4 exemplarily shows intra directional modes of 65 predictiondirections.

FIG. 5 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

FIG. 6 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

FIG. 8 is a diagram illustrating a block shape to which the LFNST isapplied.

FIG. 9 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example.

FIG. 10 shows that the number of output data for the forward LFNST islimited to a maximum of 16 according to an example.

FIG. 11 is a diagram illustrating the zero-out in a block to which the4×4 LFNST is applied according to an example.

FIG. 12 is a diagram illustrating the zero-out in a block to which the8×8 LFNST is applied according to an example.

FIG. 13 is a diagram illustrating the zero-out in a block to which the8×8 LFNST is applied according to another example.

FIG. 14 is a diagram showing an example of a sub-block into which onecoding block is divided.

FIG. 15 is a diagram showing another example of a sub-block into whichone coding block is divided.

FIG. 16 is a diagram illustrating symmetry between an M×2 (M×1) blockand a 2×M (1×M) block according to an example.

FIG. 17 is a diagram illustrating an example of transposing a 2×M blockaccording to an example.

FIG. 18 shows a scanning order for an 8×2 or 2×8 region according to anexample.

FIG. 19 is a diagram for explaining a method of decoding an imageaccording to an example.

FIG. 20 is a diagram for explaining a method of encoding an imageaccording to an example.

FIG. 21 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 22 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

DESCRIPTION OF EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards (e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265), EVC(essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pe1 may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M×N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “/” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B, and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B, and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B, and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. In other words, the “prediction” of the presentdisclosure is not limited to “intra prediction”, and “intra prediction”may be proposed as an example of “prediction”. In addition, whenindicated as “prediction (i.e., intra prediction)”, it may also meanthat “intra prediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus applicable to embodiments of thisdocument. Hereinafter, what is referred to as the video encodingapparatus may include the image encoding apparatus.

Referring to FIG. 1, the encoding apparatus 100 may include and beconfigured with an image partitioner 110, a predictor 120, a residualprocessor 130, an entropy encoder 140, an adder 150, a filter 160, and amemory 170. The predictor 120 may include an inter predictor 121 and anintra predictor 122. The residual processor 130 may include atransformer 132, a quantizer 133, a dequantizer 134, and an inversetransformer 135. The residual processor 130 may further include asubtractor 131. The adder 150 may be referred to as a reconstructor orreconstructed block generator. The image partitioner 110, the predictor120, the residual processor 130, the entropy encoder 140, the adder 150,and the filter 160, which have been described above, may be configuredby one or more hardware components (e.g., encoder chipsets orprocessors) according to an embodiment. Further, the memory 170 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 170 as an internal/external component.

The image partitioner 110 may partition an input image (or a picture ora frame) input to the encoding apparatus 100 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pe1 ofone picture (or image).

In the encoding apparatus 100, a prediction signal (predicted block,prediction sample array) output from the inter predictor 121 or theintra predictor 122 may be subtracted from an input image signal(original block, original sample array) to generate a residual signal(residual block, residual sample array), and the generated residualsignal is transmitted to the transformer 132. In this case, as shown, aunit of subtracting a prediction signal (predicted block, predictionsample array) from the input image signal (original block, originalsample array) in the encoding apparatus 100 may be called the subtractor131. The predictor may perform prediction on a processing target block(hereinafter, referred to as ‘current block’), and may generate apredicted block including prediction samples for the current block. Thepredictor may determine whether intra prediction or inter prediction isapplied on a current block or CU basis. As discussed later in thedescription of each prediction mode, the predictor may generate variousprediction related information, such as prediction mode information, andtransmit the generated information to the entropy encoder 140. Theprediction related information may be encoded in the entropy encoder140, and be output in the form of a bitstream.

The intra predictor 122 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 122 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 121 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor121 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 121 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 120 may generate a prediction signal based on variousprediction methods to be described below. For example, for prediction onone block, the predictor may apply either intra prediction or interprediction, and, as well, apply both of intra prediction and interprediction at the same time. The latter may be called combined inter andintra prediction (CIIP). Further, the predictor may be based on an intrablock copy (IBC) prediction mode, or a palette mode in order to performprediction on a block. The IBC prediction mode or palette mode may beused for content image/video coding of a game or the like, such asscreen content coding (SCC). The IBC basically performs prediction in acurrent picture, but it may be performed similarly to inter predictionin that it derives a reference block in a current picture. That is, theIBC may use at least one of inter prediction techniques described in thepresent document. The palette mode may be regarded as an example ofintra coding or intra prediction. When the palette mode is applied, asample value in a picture may be signaled based on information on apalette index and a palette table.

The prediction signal generated through the predictor (including interpredictor 121 and/or the intra predictor 122) may be used to generate areconstructed signal or to generate a residual signal. The transformer132 may generate transform coefficients by applying a transformtechnique to the residual signal. For example, the transform techniquemay include at least one of a discrete cosine transform (DCT), adiscrete sine transform (DST), a Karhunen-Loève transform (KLT), agraph-based transform (GBT), or a conditionally non-linear transform(CNT). Here, the GBT means transform obtained from a graph whenrelationship information between pixels is represented by the graph. TheCNT means transform obtained based on a prediction signal generatedusing all previously reconstructed pixels. In addition, the transformprocess may be applied to square pixel blocks of the same size, or maybe applied to non-square blocks of varying sizes.

The quantizer 133 may quantize the transform coefficients and transmitthem to the entropy encoder 140, and the entropy encoder 140 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 133 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 140may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 140 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdocument, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be incorporated in video/image information. Thevideo/image information may be encoded through the above-describedencoding procedure, and be incorporated in the bitstream. The bitstreammay be transmitted through a network, or stored in a digital storagemedium. Here, the network may include a broadcast network, acommunication network and/or the like, and the digital storage mediummay include various storage media such as USB, SD, CD, DVD, Blu-ray,HDD, SSD, and the like. A transmitter (not shown) which transmits asignal output from the entropy encoder 140 and/or a storage (not shown)which stores it may be configured as an internal/external element of theencoding apparatus 100, or the transmitter may be included in theentropy encoder 140.

Quantized transform coefficients output from the quantizer 133 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 134 and the inverse transformer 135, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 121 or the intrapredictor 122, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 150 may be called a reconstructor or areconstructed block generator. The generated reconstruction signal maybe used for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 160 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 160 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 170, specifically inthe DPB of the memory 170. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like. As discussed later in thedescription of each filtering method, the filter 160 may generatevarious information relating to filtering, and transmit the generatedinformation to the entropy encoder 140. The information on the filteringmay be encoded in the entropy encoder 140 and output in the form of abitstream.

The modified reconstructed picture which has been transmitted to thememory 170 may be used as a reference picture in the inter predictor121. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 170 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 121. The memory170 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 121 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 170 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 122.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus applicable to embodiments of thisdocument.

Referring to FIG. 2, the decoding apparatus 200 may include and beconfigured with an entropy decoder 210, a residual processor 220, apredictor 230, an adder 240, a filter 250 and a memory 260. Thepredictor 230 may include an inter predictor 232 and an intra predictor231. The residual processor 220 may include a dequantizer 221 and aninverse transformer 221. The entropy decoder 210, the residual processor220, the predictor 230, the adder 240, and the filter 250, which havebeen described above, may be configured by one or more hardwarecomponents (e.g., decoder chipsets or processors) according to anembodiment. Further, the memory 260 may include a decoded picture buffer(DPB), and may be constituted by a digital storage medium. The hardwarecomponent may further include the memory 260 as an internal/externalcomponent.

When a bitstream including video/image information is input, thedecoding apparatus 200 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 1. For example, the decoding apparatus 200may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 200 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 200 may be reproducedthrough a reproducer.

The decoding apparatus 200 may receive a signal output from the encodingapparatus of FIG. 1 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 210. For example, the entropydecoder 210 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 210 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. The prediction related informationamong informations decoded in the entropy decoder 210 may be provided tothe predictor (inter predictor 232 and intra predictor 231), andresidual values, that is, quantized transform coefficients, on whichentropy decoding has been performed in the entropy decoder 210, andassociated parameter information may be input to the residual processor220. The residual processor 220 may derive a residual signal (residualblock, residual samples, residual sample array). Further, information onfiltering among informations decoded in the entropy decoder 210 may beprovided to the filter 250. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 200 as an internal/external element,and the receiver may be a component of the entropy decoder 210.Meanwhile, the decoding apparatus according to the present document maybe called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 210, and the sample decoder may include atleast one of the dequantizer 221, the inverse transformer 222, the adder240, the filter 250, the memory 260, the inter predictor 232, and theintra predictor 231.

The dequantizer 221 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 221 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 221 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The deqauntizer 222 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 210, and specifically may determine anintra/inter prediction mode.

The predictor 220 may generate a prediction signal based on variousprediction methods to be described below. For example, for prediction onone block, the predictor may apply either intra prediction or interprediction, and, as well, apply both of intra prediction and interprediction at the same time. The latter may be called combined inter andintra prediction (CIIP). Further, the predictor may be based on an intrablock copy (IBC) prediction mode, or a palette mode in order to performprediction on a block. The IBC prediction mode or palette mode may beused for content image/video coding of a game or the like, such asscreen content coding (SCC). The IBC basically performs prediction in acurrent picture, but it may be performed similarly to inter predictionin that it derives a reference block in a current picture. That is, theIBC may use at least one of inter prediction techniques described in thepresent document. The palette mode may be regarded as an example ofintra coding or intra prediction. When the palette mode is applied,information on a palette table and a palette index may be included inthe video/image information and signaled.

The intra predictor 231 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 231 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 232 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 232 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 240 adds obtained residual signal to a prediction signal(predicted block, predicted sample array) output from the predictor(inter predictor 232 and/or intra predictor 231), so that areconstructed signal (reconstructed picture, reconstructed block,reconstructed sample array) may be generated. When there is no residualfor a processing target block as in a case where the skip mode isapplied, the predicted block may be used as a reconstructed block.

The adder 240 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 250 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 250 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 260, specifically inthe DPB of the memory 260. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified) reconstructed picture which has been stored in the DPB ofthe memory 260 may be used as a reference picture in the inter predictor232. The memory 260 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 160 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory260 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 231.

In the present document, embodiments described in the filter 160, theinter predictor 121 and the intra predictor 122 of the encodingapparatus 100 may be similarly or correspondingly applied to the filter250, the inter predictor 232 and the intra predictor 231 of the decodingapparatus 200.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be identically derived in the encoding apparatus andthe decoding apparatus, and the encoding apparatus may increase imagecoding efficiency by signaling to the decoding apparatus not originalsample value of an original block itself but information on residual(residual information) between the original block and the predictedblock. The decoding apparatus may derive a residual block includingresidual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 3 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 3, a transformer may correspond to the transformer inthe encoding apparatus of foregoing FIG. 1, and an inverse transformermay correspond to the inverse transformer in the encoding apparatus offoregoing FIG. 1, or to the inverse transformer in the decodingapparatus of FIG. 2.

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S410). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

In other words, when the conventional transform method is applied,transform coefficients might be generated by applying transform from aspace domain to a frequency domain for a residual signal (or residualblock) based on the DCT type 2. Unlike to this, when the multiple coretransform is applied, transform coefficients (or primary transformcoefficients) may be generated by applying transform from a space domainto a frequency domain for a residual signal (or residual block) based onthe DCT type 2, the DST type 7, the DCT type 8, and/or DST type 1.Herein, the DCT type 2, the DST type 7, the DCT type 8, and the DST type1 may be called a transform type, transform kernel or transform core.These DCT/DST transform types can be defined based on basis functions.

When the multiple core transform is performed, a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform may beperformed on the target block based on the vertical transform kernel,and a horizontal transform may be performed on the target block based onthe horizontal transform kernel. Here, the horizontal transform mayindicate a transform on horizontal components of the target block, andthe vertical transform may indicate a transform on vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index for the target block (CU or subblock) including aresidual block.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST7, and atrTypeHor or trTypeVer value of 2 may be set to DCT8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that both bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_mts_idx[x0][y0] 0 1 2 3 4 trTypeHor 0 1 2 1 2 trTypeVer 0 1 12 2

The transformer may derive modified (secondary) transform coefficientsby performing the secondary transform based on the (primary) transformcoefficients (S420). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compressive expression by using a correlationexisting between (primary) transform coefficients. The secondarytransform may include a non-separable transform. In this case, thesecondary transform may be called a non-separable secondary transform(NSST), or a mode-dependent non-separable secondary transform (MDNSST).The non-separable secondary transform may represent a transform whichgenerates modified transform coefficients (or secondary transformcoefficients) for a residual signal by secondary-transforming, based ona non-separable transform matrix, (primary) transform coefficientsderived through the primary transform. At this time, the verticaltransform and the horizontal transform may not be applied separately (orhorizontal and vertical transforms may not be applied independently) tothe (primary) transform coefficients, but the transforms may be appliedat once based on the non-separable transform matrix. In other words, thenon-separable secondary transform may represent a transform method inwhich is not separately applied in the vertical direction and thehorizontal direction for the (primary) transform coefficients, and forexample, two-dimensional signals (transform coefficients) arere-arranged to a one-dimensional signal through a certain determineddirection (e.g., row-first direction or column-first direction), andthen modified transform coefficients (or secondary transformcoefficients) are generated based on the non-separable transform matrix.For example, according to a row-first order, M×N blocks are disposed ina line in an order of a first row, a second row, . . . , and an Nth row.According to a column-first order, M×N blocks are disposed in a line inan order of a first column, a second column, . . . , and an Nth column.The non-separable secondary transform may be applied to a top-leftregion of a block configured with (primary) transform coefficients(hereinafter, may be referred to as a transform coefficient block). Forexample, if the width (W) and the height (H) of the transformcoefficient block are all equal to or greater than 8, an 8×8non-separable secondary transform may be applied to a top-left 8×8region of the transform coefficient block. Further, if the width (W) andthe height (H) of the transform coefficient block are all equal to orgreater than 4, and the width (W) or the height (H) of the transformcoefficient block is less than 8, then a 4×4 non-separable secondarytransform may be applied to a top-left min(8,W)×min(8,H) region of thetransform coefficient block. However, the embodiment is not limited tothis, and for example, even if only the condition that the width (W) orheight (H) of the transform coefficient block is equal to or greaterthan 4 is satisfied, the 4×4 non-separable secondary transform may beapplied to the top-left min(8,W)×min(8,H) region of the transformcoefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector

may be represented as below.

=[X₀₀X₀₁X₀₂X₀₃X₁₀X₁₁X₁₂X₁₃X₂₀X₂₁X₂₂X₂₃X₃₀X₃₁X₃₂X₃₃]^(T)   [Equation 2]

In Equation 2, the vector

is a one-dimensional vector obtained by rearranging the two-dimensionalblock X of Equation 1 according to the row-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

=T·

  [Equation 3]

In this equation,

represents a transform coefficient vector, and T represents a 16×16(non-separable) transform matrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector

may be derived, and the

may be re-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. For example, an 8×8 transform kernel matrix may be a64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directional (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 4 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 4, on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 4, H and V denote horizontal directionality andvertical directionality, respectively, and numerals −32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 36 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 lfnstPredModeIntra lfnstTrSetIdx lfnstPredModeIntra < 0 1  0 <=lfnstPredModeIntra <= 1 0  2 <= lfnstPredModeIntra <= 12 1 13 <=lfnstPredModeIntra <= 23 2 24 <= lfnstPredModeIntra <= 44 3 45 <=lfnstPredModeIntra <= 55 2 56 <= lfnstPredModeIntra <= 80 1 81 <=lfnstPredModeIntra <= 83 0

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S450), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S460). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, since theRST is mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 135 of the encoding apparatus 100 and theinverse transformer 222 of the decoding apparatus 200 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 5 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 100 and thedecoding apparatus 200, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{RxN} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & & t_{1N} \\t_{21} & t_{22} & t_{23} & \ldots & t_{2N} \\ & \vdots & & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \cdots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

The matrix T in the Reduced Transform block shown in FIG. 5(a) may meanthe matrix T_(R×N) of Equation 4. As shown in FIG. 5(a), when thereduced transform matrix T_(R×N) is multiplied to residual samples forthe target block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N= 16/64=¼), then the RST according toFIG. 5(a) may be expressed as a matrix operation as shown in Equation 5below. In this case, memory and multiplication calculation can bereduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & \ldots & t_{2,64} \\ & \vdots & & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \cdots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\ \vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

In Equation 5, r₁ to r₆₄ may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients ci for the target block may be derived, and aprocess of deriving ci may be as in Equation 6.

[Equation 6]   for i from to R:   a=0   for j from 1 to N    a +=t_(ij) * g

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(N×1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 100 to the decodingapparatus 200 decreases, so efficiency of transmission between theencoding apparatus 100 and the decoding apparatus 200 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 132 of the encoding apparatus 100 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 200,and the inverse transformer 222 of the decoding apparatus 200 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix T_(N×R) according to an example isN×R less than the size N×N of the regular inverse transform matrix, andis in a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix T^(t) in the Reduced Inv. Transform block shown in FIG. 5(b)may mean the inverse RST matrix T_(R×N) ^(T) (the superscript T meanstranspose). When the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block as shown in FIG. 5(b),the modified transform coefficients for the target block or the residualsamples for the current block may be derived. The inverse RST matrixT_(R×N) ^(T) may be expressed as (T_(R×N) ^(T))_(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix T_(R×N) ^(T) ismultiplied to the transform coefficients for the target block.Meanwhile, the inverse RST may be applied as the inverse primarytransform, and in this case, the residual samples for the target blockmay be derived when the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N= 16/64=¼), then the RST accordingto FIG. 5(b) may be expressed as a matrix operation as shown in Equation7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{2,1} & & t_{16,1} \\t_{1,2} & t_{2,2} & & t_{16,2} \\t_{1,3} & t_{2,3} & \cdots & t_{16,3} \\ \vdots & \vdots & & \vdots \\ & \vdots & \ddots & \vdots \\t_{1,64} & t_{2,64} & \cdots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\ \vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to c₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

[Equation 8]   For i from 1 to N  r_(i)=0   for j from 1 to R    n +=t_(ji) * c_(j)

As a result of the calculation of Equation 8, r₁ to r_(N) representingthe modified transform coefficients for the target block or the residualsamples for the target block may be derived. When considered from theviewpoint of the size of the inverse transform matrix, the size of theregular inverse transform matrix is 64×64 (N×N), but the size of thereduced inverse transform matrix is reduced to 64×16 (R×N), so memoryusage in a case of performing the inverse RST can be reduced by an R/Nratio when compared with a case of performing the regular inversetransform. In addition, when compared to the number of multiplicationcalculations N×N in a case of using the regular inverse transformmatrix, the use of the reduced inverse transform matrix can reduce thenumber of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block when both W and H ofthe target block to be transformed are equal to or greater than 8, andthe 8×8 region may be a top-left 8×8 region in the transform coefficientblock. Similarly, a 4×4 lfnst and a 4×4 RST refer to transformsapplicable to a 4×4 region included in the transform coefficient blockwhen both W and H of the target block to are equal to or greater than 4,and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m≤16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in the inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 135 of the encoding apparatus 100 and the inversetransformer 222 of the decoding apparatus 200 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform on the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

The above-described non-separated transform, the LFNST, will bedescribed in detail as follows. The LFNST may include a forwardtransform by the encoding apparatus and an inverse transform by thedecoding apparatus.

The encoding apparatus receives a result (or a part of a result) derivedafter applying a primary (core) transform as an input, and applies aforward secondary transform (secondary transform).

y=G ^(T) x   [Equation 9]

In Equation 9, x and y are inputs and outputs of the secondarytransform, respectively, and G is a matrix representing the secondarytransform, and transform basis vectors are composed of column vectors.In the case of an inverse LFNST, when the dimension of thetransformation matrix G is expressed as [number of rows×number ofcolumns], in the case of an forward LFNST, the transposition of matrix Gbecomes the dimension of G^(T).

For the inverse LFNST, the dimensions of matrix G are [48×16], [48×8],[16×16], [16×8], and the [48×8] matrix and the [16×8] matrix are partialmatrices that sampled 8 transform basis vectors from the left of the[48×16] matrix and the [16×16] matrix, respectively.

On the other hand, for the forward LFNST, the dimensions of matrix G^(T)are [16×48], [8×48], [16×16], [8×16], and the [8×48] matrix and the[8×16] matrix are partial matrices obtained by sampling 8 transformbasis vectors from the top of the [16×48] matrix and the [16×16] matrix,respectively.

Therefore, in the case of the forward LFNST, a [48×1] vector or [16×1]vector is possible as an input x, and a [16×1] vector or a [8×1] vectoris possible as an output y. In video coding and decoding, the output ofthe forward primary transform is two-dimensional (2D) data, so toconstruct the [48×1] vector or the [16×1] vector as the input x, aone-dimensional vector must be constructed by properly arranging the 2Ddata that is the output of the forward transformation.

FIG. 6 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example. The left diagrams of (a) and (b) of FIG. 6 show thesequence for constructing a [48×1] vector, and the right diagrams of (a)and (b) of FIG. 6 shows the sequence for constructing a [16×1] vector.In the case of the LFNST, a one-dimensional vector x can be obtained bysequentially arranging 2D data in the same order as in (a) and (b) ofFIG. 6.

The arrangement direction of the output data of the forward primarytransform may be determined according to an intra prediction mode of thecurrent block. For example, when the intra prediction mode of thecurrent block is in the horizontal direction with respect to thediagonal direction, the output data of the forward primary transform maybe arranged in the order of (a) of FIG. 6, and when the intra predictionmode of the current block is in the vertical direction with respect tothe diagonal direction, the output data of the forward primary transformmay be arranged in the order of (b) of FIG. 6.

According to an example, an arrangement order different from thearrangement orders of (a) and (b) FIG. 6 may be applied, and in order toderive the same result (y vector) as when the arrangement orders of (a)and (b) FIG. 6 is applied, the column vectors of the matrix G may berearranged according to the arrangement order. That is, it is possibleto rearrange the column vectors of G so that each element constitutingthe x vector is always multiplied by the same transform basis vector.

Since the output y derived through Equation 9 is a one-dimensionalvector, when two-dimensional data is required as input data in theprocess of using the result of the forward secondary transformation asan input, for example, in the process of performing quantization orresidual coding, the output y vector of Equation 9 must be properlyarranged as 2D data again.

FIG. 7 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

In the case of the LFNST, output values may be arranged in a 2D blockaccording to a predetermined scan order. (a) of FIG. 7 shows that whenthe output y is a [16×1] vector, the output values are arranged at 16positions of the 2D block according to a diagonal scan order. (b) ofFIG. 7 shows that when the output y is a [8×1] vector, the output valuesare arranged at 8 positions of the 2D block according to the diagonalscan order, and the remaining 8 positions are filled with zeros. X in(b) of FIG. 7 indicates that it is filled with zero.

According to another example, since the order in which the output vectory is processed in performing quantization or residual coding may bepreset, the output vector y may not be arranged in the 2D block as shownin FIG. 7. However, in the case of the residual coding, data coding maybe performed in 2D block (eg, 4×4) units such as CG (Coefficient Group),and in this case, the data are arranged according to a specific order asin the diagonal scan order of FIG. 7.

Meanwhile, the decoding apparatus may configure the one-dimensionalinput vector y by arranging two-dimensional data output through adequantization process or the like according to a preset scan order forthe inverse transformation. The input vector y may be output as theoutput vector x by the following equation.

x=Gy   [Equation 10]

In the case of the inverse LFNST, an output vector x can be derived bymultiplying an input vector y, which is a [16×1] vector or a [8×1]vector, by a G matrix. For the inverse LFNST, the output vector x can beeither a [48×1] vector or a [16×1] vector.

The output vector x is arranged in a two-dimensional block according tothe order shown in FIG. 6 and is arranged as two-dimensional data, andthis two-dimensional data becomes input data (or a part of input data)of the inverse primary transformation.

Accordingly, the inverse secondary transformation is the opposite of theforward secondary transformation process as a whole, and in the case ofthe inverse transformation, unlike in the forward direction, the inversesecondary transformation is first applied, and then the inverse primarytransformation is applied.

In the inverse LFNST, one of 8 [48×16] matrices and 8 [16×16] matricesmay be selected as the transformation matrix G. Whether to apply the[48×16] matrix or the [16×16] matrix depends on the size and shape ofthe block.

In addition, 8 matrices may be derived from four transform sets as shownin Table 2 above, and each transform set may consist of two matrices.Which transform set to use among the 4 transform sets is determinedaccording to the intra prediction mode, and more specifically, thetransform set is determined based on the value of the intra predictionmode extended by considering the Wide Angle Intra Prediction (WAIP).Which matrix to select from among the two matrices constituting theselected transform set is derived through index signaling. Morespecifically, 0, 1, and 2 are possible as the transmitted index value, 0may indicate that the LFNST is not applied, and 1 and 2 may indicate anyone of two transform matrices constituting a transform set selectedbased on the intra prediction mode value.

Meanwhile, as described above, which transform matrix of the [48×16]matrix and the [16×16] matrix is applied to the LFNST is determined bythe size and shape of the transform target block.

FIG. 8 is a diagram illustrating a block shape to which the LFNST isapplied. (a) of FIG. 8 shows 4×4 blocks, (b) shows 4×8 and 8×4 blocks,(c) shows 4×N or N×4 blocks in which N is 16 or more, (d) shows 8×8blocks, (e) shows M×N blocks where M≥8, N≥8, and N>8 or M>8.

In FIG. 8, blocks with thick borders indicate regions to which the LFNSTis applied. For the blocks of FIGS. 10 (a) and (b), the LFNST is appliedto the top-left 4×4 region, and for the block of FIG. 8 (c), the LFNSTis applied individually the two top-left 4×4 regions are continuouslyarranged. In (a), (b), and (c) of FIG. 8, since the LFNST is applied inunits of 4×4 regions, this LFNST will be hereinafter referred to as “4×4LFNST”. Based on the matrix dimension for G, a [16×16] or [16×8] matrixmay be applied.

More specifically, the [16×8] matrix is applied to the 4×4 block (4×4 TUor 4×4 CU) of FIG. 8 (a) and the [16×16] matrix is applied to the blocksin (b) and (c) of FIG. 8. This is to adjust the computational complexityfor the worst case to 8 multiplications per sample.

With respect to (d) and (e) of FIG. 8, the LFNST is applied to thetop-left 8×8 region, and this LFNST is hereinafter referred to as “8×8LFNST”. As a corresponding transformation matrix, a [48×16] matrix or[48×8] matrix may be applied. In the case of the forward LFNST, sincethe [48×1] vector (x vector in Equation 9) is input as input data, allsample values of the top-left 8×8 region are not used as input values ofthe forward LFNST. That is, as can be seen in the left order of FIG. 6(a) or the left order of FIG. 6 (b), the [48×1] vector may beconstructed based on samples belonging to the remaining 3 4×4 blockswhile leaving the bottom-right 4×4 block as it is.

The [48×8] matrix may be applied to an 8×8 block (8×8 TU or 8×8 CU) inFIG. 8 (d), and the [48×16] matrix may be applied to the 8×8 block inFIG. 8(e). This is also to adjust the computational complexity for theworst case to 8 multiplications per sample.

Depending on the block shape, when the corresponding forward LFNST (4×4LFNST or 8×8 LFNST) is applied, 8 or 16 output data (y vector inEquation 9, [8×1] or [16×1] vector) is generated. In the forward LFNST,the number of output data is equal to or less than the number of inputdata due to the characteristics of the matrix G^(T).

FIG. 9 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example, and shows a block in which outputdata of the forward LFNST is arranged according to a block shape.

The shaded area at the top-left of the block shown in FIG. 9 correspondsto the area where the output data of the forward LFNST is located, thepositions marked with 0 indicate samples filled with 0 values, and theremaining area represents regions that are not changed by the forwardLFNST. In the area not changed by the LFNST, the output data of theforward primary transform remains unchanged.

As described above, since the dimension of the transform matrix appliedvaries according to the shape of the block, the number of output dataalso varies. As FIG. 9, the output data of the forward LFNST may notcompletely fill the top-left 4×4 block. In the case of (a) and (d) ofFIG. 9, a [16×8] matrix and a [48×8] matrix are applied to the blockindicated by a thick line or a partial region inside the block,respectively, and a [8×1] vector as the output of the forward LFNST isgenerated. That is, according to the scan order shown in (b) of FIG. 7,only 8 output data may be filled as shown in (a) and (d) of FIGS. 9, and0 may be filled in the remaining 8 positions. In the case of the LFNSTapplied block of FIG. 8 (d), as shown in FIG. 9(d), two 4×4 blocks inthe top-right and bottom-left adjacent to the top-left 4×4 block arealso filled with 0 values.

As described above, basically, by signaling the LFNST index, whether toapply the LFNST and the transform matrix to be applied are specified. Asshown FIG. 9, when the LFNST is applied, since the number of output dataof the forward LFNST may be equal to or less than the number of inputdata, a region filled with a zero value occurs as follows.

1) As shown in (a) of FIG. 9, samples from the 8th and later positionsin the scan order in the top-left 4×4 block, that is, samples from the9th to the 16th.

2) As shown in (d) and (e) of FIG. 9, when the [48×16] matrix or the[48×8] matrix is applied, two 4×4 blocks adjacent to the top-left 4×4block or the second and third 4×4 blocks in the scan order.

Therefore, if non-zero data exists by checking the areas 1) and 2), itis certain that the LFNST is not applied, so that the signaling of thecorresponding LFNST index can be omitted.

According to an example, for example, in the case of LFNST adopted inthe VVC standard, since signaling of the LFNST index is performed afterthe residual coding, the encoding apparatus may know whether there isthe non-zero data (significant coefficients) for all positions withinthe TU or CU block through the residual coding. Accordingly, theencoding apparatus may determine whether to perform signaling on theLFNST index based on the existence of the non-zero data, and thedecoding apparatus may determine whether the LFNST index is parsed. Whenthe non-zero data does not exist in the area designated in 1) and 2)above, signaling of the LFNST index is performed.

Since a truncated unary code is applied as a binarization method for theLFNST index, the LFNST index consists of up to two bins, and 0, 10, and11 are assigned as binary codes for possible LFNST index values of 0, 1,and 2, respectively. In the case of the LFNST currently adopted for VVC,a context-based CABAC coding is applied to the first bin (regularcoding), and a bypass coding is applied to the second bin. The totalnumber of contexts for the first bin is 2, when (DCT-2, DCT-2) isapplied as a primary transform pair for the horizontal and verticaldirections, and a luma component and a chroma component are coded in adual tree type, one context is allocated and another context applies forthe remaining cases. The coding of the LFNST index is shown in a tableas follows.

TABLE 3 Syntax binIdx element 0 1 2 3 4 >=5 lfnst_idx[ ][ ] {tu_mts_idx[ x0 ][ y0 ] bypass na na na na = = 0 && treeType !=SINGLE_TREE ) ? 1 : 0

Meanwhile, for the adopted LFNST, the following simplification methodsmay be applied.

(i) According to an example, the number of output data for the forwardLFNST may be limited to a maximum of 16.

In the case of (c) of FIG. 8, the 4×4 LFNST may be applied to two 4×4regions adjacent to the top-left, respectively, and in this case, amaximum of 32 LFNST output data may be generated. when the number ofoutput data for forward LFNST is limited to a maximum of 16, in the caseof 4×N/N×4 (N≥16) blocks (TU or CU), the 4×4 LFNST is only applied toone 4×4 region in the top-left, the LFNST may be applied only once toall blocks of FIG. 8. Through this, the implementation of image codingmay be simplified.

FIG. 10 shows that the number of output data for the forward LFNST islimited to a maximum of 16 according to an example. As FIG. 10, when theLFNST is applied to the most top-left 4×4 region in a 4×N or N×4 blockin which N is 16 or more, the output data of the forward LFNST becomes16 pieces.

(ii) According to an example, zero-out may be additionally applied to aregion to which the LFNST is not applied. In this document, the zero-outmay mean filling values of all positions belonging to a specific regionwith a value of 0. That is, the zero-out can be applied to a region thatis not changed due to the LFNST and maintains the result of the forwardprimary transformation. As described above, since the LFNST is dividedinto the 4×4 LFNST and the 8×8 LFNST, the zero-out can be divided intotwo types ((ii)-(A) and (ii)-(B)) as follows.

(ii)-(A) When the 4×4 LFNST is applied, a region to which the 4×4 LFNSTis not applied may be zeroed out. FIG. 11 is a diagram illustrating thezero-out in a block to which the 4×4 LFNST is applied according to anexample.

As shown in FIG. 11, with respect to a block to which the 4×4 LFNST isapplied, that is, for all of the blocks in (a), (b) and (c) of FIG. 9,the whole region to which the LFNST is not applied may be filled withzeros.

On the other hand, (d) of FIG. 11 shows that when the maximum value ofthe number of the output data of the forward LFNST is limited to 16 asshown in FIG. 10, the zero-out is performed on the remaining blocks towhich the 4×4 LFNST is not applied.

(ii)-(B) When the 8×8 LFNST is applied, a region to which the 8×8 LFNSTis not applied may be zeroed out. FIG. 12 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according to anexample.

As shown in FIG. 12, with respect to a block to which the 8×8 LFNST isapplied, that is, for all of the blocks in (d) and (e) of FIG. 9, thewhole region to which the LFNST is not applied may be filled with zeros.

(iii) Due to the zero-out presented in (ii) above, the area filled withzeros may be not same when the LFNST is applied. Accordingly, it ispossible to check whether the non-zero data exists according to thezero-out proposed in (ii) over a wider area than the case of the LFNSTof FIG. 9.

For example, when (ii)-(B) is applied, after checking whether thenon-zero data exists where the area filled with zero values in (d) and(e) of FIG. 9 in addition to the area filled with 0 additionally in FIG.12, signaling for the LFNST index can be performed only when thenon-zero data does not exist.

Of course, even if the zero-out proposed in (ii) is applied, it ispossible to check whether the non-zero data exists in the same way asthe existing LFNST index signaling. That is, after checking whether thenon-zero data exists in the block filled with zeros in FIG. 9, the LFNSTindex signaling may be applied. In this case, the encoding apparatusonly performs the zero out and the decoding apparatus does not assumethe zero out, that is, checking only whether the non-zero data existsonly in the area explicitly marked as 0 in FIG. 9, may perform the LFNSTindex parsing.

Alternatively, according to another example, the zero-out may beperformed as shown in FIG. 13. FIG. 13 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according toanother example.

As shown in FIGS. 11 and 12, the zero-out may be applied to all regionsother than the region to which the LFNST is applied, or the zero-out maybe applied only to a partial region as shown in FIG. 13. The zero-out isapplied only to regions other than the top-left 8×8 region of FIG. 13,the zero-out may not be applied to the bottom-right 4×4 block within thetop-left 8×8 region.

Various embodiments in which combinations of the simplification methods((i), (ii)-(A), (ii)-(B), (iii)) for the LFNST are applied may bederived. Of course, the combinations of the above simplification methodsare not limited to the following embodiment, and any combination may beapplied to the LFNST.

Embodiment

-   -   Limit the number of output data for forward LFNST to a maximum        of 16→(i)    -   When the 4×4 LFNST is applied, all areas to which the 4×4 LFNST        is not applied are zero-out→(ii)-(A)    -   When the 8×8 LFNST is applied, all areas to which the 8×8 LFNST        is not applied are zero-out→(ii)-(B)    -   After checking whether the non-zero data exists also the        existing area filled with zero value and the area filled with        zeros due to additional zero outs ((ii)-(A), (ii)-(B)), the        LFNST index is signaled only when the non-zero data does not        exist→(iii)

In the case of Embodiment, when the LFNST is applied, an area in whichthe non-zero output data can exist is limited to the inside of thetop-left 4×4 area. In more detail, in the case of FIG. 11 (a) and FIG.12 (a), the 8th position in the scan order is the last position wherenon-zero data can exist. In the case of FIG. 11 (b) and (c) and FIG. 12(b), the 16th position in the scan order (ie, the position of thebottom-right edge of the top-left 4×4 block) is the last position wheredata other than 0 may exist.

Therefore, when the LFNST is applied, after checking whether thenon-zero data exists in a position where the residual coding process isnot allowed (at a position beyond the last position), it can bedetermined whether the LFNST index is signaled.

In the case of the zero-out method proposed in (ii), since the number ofdata finally generated when both the primary transform and the LFNST areapplied, the amount of computation required to perform the entiretransformation process can be reduced. That is, when the LFNST isapplied, since zero-out is applied to the forward primary transformoutput data existing in a region to which the LFNST is not applied,there is no need to generate data for the region that become zero-outduring performing the forward primary transform. Accordingly, it ispossible to reduce the amount of computation required to generate thecorresponding data. The additional effects of the zero-out methodproposed in (ii) are summarized as follows.

First, as described above, the amount of computation required to performthe entire transform process is reduced.

In particular, when (ii)-(B) is applied, the amount of calculation forthe worst case is reduced, so that the transform process can belightened. In other words, in general, a large amount of computation isrequired to perform a large-size primary transformation. By applying(ii)-(B), the number of data derived as a result of performing theforward LFNST can be reduced to 16 or less. In addition, as the size ofthe entire block (TU or CU) increases, the effect of reducing the amountof transform operation is further increased.

Second, the amount of computation required for the entire transformprocess can be reduced, thereby reducing the power consumption requiredto perform the transform.

Third, the latency involved in the transform process is reduced.

The secondary transformation such as the LFNST adds a computationalamount to the existing primary transformation, thus increasing theoverall delay time involved in performing the transformation. Inparticular, in the case of intra prediction, since reconstructed data ofneighboring blocks is used in the prediction process, during encoding,an increase in latency due to a secondary transformation leads to anincrease in latency until reconstruction. This can lead to an increasein overall latency of intra prediction encoding.

However, if the zero-out suggested in (ii) is applied, the delay time ofperforming the primary transform can be greatly reduced when LFNST isapplied, the delay time for the entire transform is maintained orreduced, so that the encoding apparatus can be implemented more simply.

Meanwhile, in the conventional intra prediction, a coding target blockis regarded as one coding unit, and coding is performed withoutpartition thereof. However, the ISP (Intra Sub-Partitions) coding refersto performing the intra prediction coding with the coding target blockbeing partitioned in a horizontal direction or a vertical direction. Inthis case, a reconstructed block may be generated by performingencoding/decoding in units of partitioned blocks, and the reconstructedblock may be used as a reference block of the next partitioned block.According to an example, in the ISP coding, one coding block may bepartitioned into two or four sub-blocks and be coded, and in the ISP,intra prediction is performed on one sub-block by referring to thereconstructed pixel value of a sub-block located adjacent to the left ortop side thereof. Hereinafter, the term “coding” may be used as aconcept including both coding performed by the encoding apparatus anddecoding performed by the decoding apparatus.

Table 4 shows the number of sub-blocks partitioned according to blocksizes when ISP is applied, and sub-partitions partitioned according toISP may be referred to as transform blocks (TUs).

TABLE 4 Block size Number of (CU) partitions 4 × 4 not available 4 × 8,8 × 4 2 All other cases 4

The ISP partitions a block predicted as luma intra into two or foursub-partitionings in a vertical direction or a horizontal directionaccording to the size of the block. For example, the minimum block sizeto which the ISP can be applied is 4×8 or 8×4. If the block size isgreater than 4×8 or 8×4, the block is partitioned into foursub-partitionings.

FIGS. 14 and 15 show an example of a sub-block into which one codingblock is partitioned, and more specifically, FIG. 14 is an example ofpartition for a case in which a coding block (width (W)×height (H)) is a4×8 block or an 8×4 block, and FIG. 15 shows an example of partition fora case in which a coding block is not a 4×8 block, nor an 8×4 block, nora 4×4 block.

When the ISP is applied, the sub-blocks are sequentially coded accordingto the partition type, such as, horizontally or vertically, from left toright, or from top to bottom, and coding for the next sub-block may beperformed after performing up to a restoration process through inversetransform and intra prediction for one sub-block. For the leftmost oruppermost sub-block, as in a conventional intra prediction method, thereconstructed pixel of the coding block which has been already coded isreferred to. Additionally, if the previous sub-block is not adjacent toeach side of an internal sub-block that follows it, in order to derivereference pixels adjacent to a corresponding side, as in theconventional intra prediction method, the reconstructed pixel of analready coded adjacent coding block is referred to.

In the ISP coding mode, all sub-blocks may be coded with the same intraprediction mode, and a flag indicating whether or not to use the ISPcoding and a flag indicating in which direction (horizontal or vertical)partition is to be performed may be signaled. As in FIGS. 14 and 15, thenumber of sub-blocks may be adjusted to 2 or 4 depending on the blockshape, and when the size (width×height) of one sub-block is less than16, the partition may not be allowed for the corresponding sub-blocks,nor the application of the ISP coding itself may be restricted.

Meanwhile, in the case of ISP prediction mode, one coding unit ispartitioned into two or four partition blocks, that is, sub-blocks, andpredicted, and the same intra prediction mode is applied to the thuspartitioned two or four partition blocks.

As described above, both a horizontal direction (if an M×N coding unithaving a horizontal length and a vertical length of M and N,respectively, is divided in the horizontal direction, it is divided intoM×(N/2) blocks when divided into two, and into an M×(N/4) blocks whendivided into four) and a vertical direction (if the M×N coding unit isdivided in the vertical direction, it is divided into (M/2)×N blockswhen divided into two, and divided into (M/4)×N blocks when divided intofour) are possible as the partition direction. When partitioned in thehorizontal direction, partition blocks are coded in an order from top todown, and when partitioned in the vertical direction, partition blocksare coded in an order from left to right. The currently coded partitionblock may be predicted by referring to the reconstructed pixel values ofthe top (left) partition block in the case of the horizontal (vertical)direction partition.

Transformation may be applied to the residual signal generated by theISP prediction method in units of partition blocks. MTS (MultipleTransform Selection) technology based on the DST-7/DCT-8 combination aswell as the existing DCT-2 may be applied to the primary transform (coretransform or primary transform) based on the forward direction, and anLFNST (Low Frequency Non-Separable Transform) may be applied to atransform coefficient generated according to the primary transform togenerate a final modified transform coefficient.

That is, LFNST may also be applied to partition blocks divided byapplying the ISP prediction mode, and the same intra prediction mode isapplied to the divided partition blocks as described above. Accordingly,when selecting the LFNST set derived based on the intra prediction mode,the derived LFNST set may be applied to all partition blocks. That is,the same intra prediction mode is applied to all partition blocks, andthereby the same LFNST set may be applied to all partition blocks.

Meanwhile, according to an example, the LFNST may be applied only totransform blocks having both a horizontal and vertical length of 4 ormore. Therefore, when the horizontal or vertical length of the partitionblock partitioned according to the ISP prediction method is less than 4,the LFNST is not applied and the LFNST index is not signaled.Additionally, when the LFNST is applied to each partition block, thecorresponding partition block may be regarded as one transform block. Ofcourse, when the ISP prediction method is not applied, the LFNST may beapplied to the coding block.

Application of the LFNST to each partition block is described in detailas follows.

According to an example, after applying the forward LFNST to anindividual partition block, and after leaving only up to 16 coefficients(8 or 16) in the top-left 4×4 region according to the transformcoefficient scanning order, zero-out of filling all remaining positionsand regions with a value of 0 may be applied.

Alternatively, according to an example, when the length of one side ofthe partition block is 4, the LFNST is applied only to the top-left 4×4region, and when the length of all sides of the partition block, thatis, the width and height, are 8 or more, the LFNST may be applied to theremaining 48 coefficients except for a bottom-right 4×4 region in atop-left 8×8 region.

Alternatively, according to an example, in order to adjust thecomputational complexity of the worst case to 8 multiplications persample, when each partition block is 4×4 or 8×8, only 8 transformcoefficients may be output after applying the forward LFNST. That is, ifthe partition block is 4×4, an 8×16 matrix may be applied as a transformmatrix, and if the partition block is 8×8, an 8×48 matrix may be appliedas a transform matrix.

Meanwhile, in the current VVC standard, LFNST index signaling isperformed in units of coding units. Accordingly, when the ISP predictionmode is used and the LFNST is applied to all partition blocks, then thesame LFNST index value may be applied to the corresponding partitionblocks. That is, when the LFNST index value is transmitted once at thecoding unit level, the corresponding LFNST index may be applied to allpartition blocks in the coding unit. As described above, the LFNST indexvalue may have values of 0, 1, and 2, 0 indicates a case in which theLFNST is not applied, and 1 and 2 indicate two transform matricespresent in one LFNST set when the LFNST is applied.

As described above, the LFNST set is determined by the intra predictionmode, and since all partition blocks in the coding unit are predicted inthe same intra prediction mode in the case of the ISP prediction mode,the partition blocks may refer to the same LFNST set.

As another example, the LFNST index signaling is still performed inunits of coding units, but in the case of the ISP prediction mode,without determining whether or not to apply the LFNST uniformly to allpartition blocks, whether to apply the LFNST index value signaled at thecoding unit level to each partition block or not to apply the LFNST maybe determined through a separate condition. Here, the separate conditionmay be signaled in the form of a flag for each partition block throughthe bitstream, and when the flag value is 1, the LFNST index valuesignaled at the coding unit level may be applied, and when the flagvalue is 0, the LFNST may not be applied.

Meanwhile, in the coding unit to which the ISP mode is applied, anexample of applying the LFNST when the length of one side of thepartition block is less than 4 is discussed as follows.

First, when the size of the partition block is N×2 (2×N), the LFNST maybe applied to the top-left M×2 (2×M) region (here, M≤N). For example,when M=8, the corresponding top-left region becomes 8×2 (2×8), and thus,the region in which 16 residual signals exist may be the input of theforward LFNST, and the R×16 (R≤16) forward transformation matrix may beapplied.

Here, the forward LFNST matrix may not be the matrix included in thecurrent VVC standard, but a separate additional matrix. In addition, forcomplexity adjustment of the worst case, an 8×16 matrix obtained bysampling only the upper 8 row vectors of the 16×16 matrix may be usedfor the transform. The complexity adjustment method will be described indetail later.

Second, when the size of the partition block is N×1 (1×N), the LFNST maybe applied to the top-left M×1 (1×M) region (here, M≤N). For example,when M=16, the corresponding top-left region becomes 16×1 (1×16), andthus, the region in which 16 residual signals exist may be the input ofthe forward LFNST, and the R×16 (R≤16) forward transformation matrix maybe applied.

Here, the corresponding forward LFNST matrix may not be the matrixincluded in the current VVC standard, but a separate additional matrix.In addition, for complexity adjustment of the worst case, an 8×16 matrixobtained by sampling only the upper 8 row vectors of the 16×16 matrixmay be used for the transform. The complexity adjustment method will bedescribed in detail later.

The first embodiment and the second embodiment may be appliedsimultaneously, or either one of the two embodiments may be applied. Inparticular, in the case of the second embodiment, since theone-dimensional transform is considered in the LFNST, it was observedthrough experiments that the compression performance improvement whichcould be obtained from the existing LFNST was not relatively greatcompared to the LFNST index signaling cost. However, in the case of thefirst embodiment, a compression performance improvement similar to thatobtained from the conventional LFNST was observed, that is, in the caseof ISP, it can be verified through experiments that the application ofLFNST for 2×N and N×2 contributes to the actual compression performance

In the LFNST in the current VVC, symmetry between intra prediction modesis applied. The same LFNST set is applied to the two directional modescentered on mode 34 (prediction in the bottom-right 45 degree diagonaldirection), and for example, the same LFNST set is applied to mode 18(horizontal direction prediction mode) and mode 50 (vertical directionprediction mode). However, in modes 35 to 66, when the forward LFNST isapplied, input data is transposed, and then the LFNST is applied.

Meanwhile, VVC supports a Wide Angle Intra Prediction (WAIP) mode, andthe LFNST set is derived based on the modified intra prediction mode inconsideration of the WAIP mode. For the modes extended by WAIP, theLFNST set is also determined by utilizing symmetry as in the generalintra prediction direction mode. For example, mode −1 is symmetric withmode 67, so the same LFNST set is applied, and mode −14 is symmetricwith mode 80, so the same LFNST set is applied. Modes 67 to 80 applyLFNST transform after transposing input data before applying the forwardLFNST.

In the case of the LFNST applied to the top-left M×2 (M×1) block, theabove-described symmetry to the LFNST cannot be applied, because theblock to which the LFNST is applied is non-square. Therefore, instead ofapplying the symmetry based on the intra prediction mode as in the LFNSTof Table 2, the symmetry between the M×2 (M×1) block and the 2×M (1×M)block may be applied.

FIG. 16 is a diagram illustrating symmetry between an M×2 (M×1) blockand a 2×M (1×M) block according to an example.

As shown in FIG. 16, mode 2 in the M×2 (M×1) block can be regarded assymmetric with mode 66 in the 2×M (1×M) block, and thus, the same LFNSTset may be applied to the 2×M (1×M) block and the M×2 (M×1) block.

At this time, in order to apply the LFNST set, which has been applied tothe M×2 (M×1) block, to the 2×M (1×M) block, the LFNST set is selectedbased on the mode 2 instead of the mode 66. That is, before applying theforward LFNST, it is possible to apply the LFNST after transposing theinput data of the 2×M (1×M) block.

FIG. 17 is a diagram illustrating an example of transposing a 2×M blockaccording to an example.

FIG. 17A is a diagram illustrating that the LFNST can be applied byreading input data in a column-first order with respect to a 2×M block,and FIG. 17B is a diagram illustrating that the LFNST is applied byreading input data in a row-first order with respect to an M×2 (M×1)block. The method of applying the LFNST to the top-left M×2 (M×1) or 2×M(M×1) block is summarized as follows.

1. First, as shown in FIGS. 17A and 17B, input data is arranged toconstruct an input vector of the forward LFNST. For example, referringto FIG. 16, for the M×2 block predicted in mode 2, the order in FIG.17(b) is followed, and for a 2×M block predicted in the mode 66, afterarranging input data according to the order of FIG. 17(a), the LFNST setfor mode 2 may be applied.

2. For the M×2 (M×1) block, the LFNST set is determined based on themodified intra prediction mode in consideration of the WAIP. Asdescribed above, a predetermined mapping relationship is establishedbetween the intra prediction mode and the LFNST set, and may berepresented by a mapping table as shown in Table 2.

For a 2×M (1×M) block, after obtaining a symmetrical mode with respectto the prediction mode (mode 34 in the case of the VVC standard) in aright downward 45 degree diagonal direction from the intra predictionmode modified in consideration of the WAIP, the LFNST set is determinedbased on the corresponding symmetric mode and the mapping table. Asymmetrical mode (y) with respect to mode 34 may be derived through thefollowing equation. The mapping table is described in more detail below.

if 2≤x≤66, y=8−x,

otherwise (x≤−1 or x≥67), y=66−x

3. When the forward LFNST is applied, the transform coefficient may bederived by multiplying the input data prepared through process 1 by theLFNST kernel. The LFNST kernel may be selected from the LFNST setdetermined in process 2 and a predetermined LFNST index.

For example, if M=8 and a 16×16 matrix is applied as the LFNST kernel,then 16 transform coefficients may be generated by multiplying thematrix by 16 input data. The generated transform coefficients may bearranged in the top-left 8×2 or 2×8 region according to the scanningorder used in the VVC standard.

FIG. 18 shows a scanning order for an 8×2 or 2×8 region according to anexample.

All regions other than the top-left 8×2 or 2×8 region may be filled withzero values (zero-out) or the existing transform coefficient to whichthe primary transform has been applied may be maintained as it is. Thepredetermined LFNST index may be one of the LFNST index values (0, 1, 2)attempted when calculating the RD cost while changing the LFNST indexvalue in the encoding process.

For a configuration that brings the worst-case computational complexitybelow a certain level (e.g. 8 multiplications/sample), for example,after generating only eight transform coefficients by multiplying an8×16 matrix obtained by taking only the upper eight rows of the 16×16matrix, the eight transform coefficients may be arranged according tothe scanning order as shown in FIG. 18, and zero-out may also be appliedto the remaining coefficient regions. The complexity adjustment for theworst case will be described later.

4. When applying the backward LFNST, a predetermined number (e.g., 16)of transform coefficients is set as an input vector, and after selectingthe LFNST kernel (e.g., 16×16 matrix) derived from the LFNST setobtained from process 2 and the parsed LFNST index, the output vectormay be derived by multiplying the LFNST kernel and the input vector.

In the case of an M×2 (M×1) block, the output vector may be arrangedaccording to the row-first order as shown in FIG. 17B, and in the caseof a 2×M (1×M) block, the output vector may be arranged according to thecolumn-first order as shown in FIG. 17A.

For the remaining area except for the area where the correspondingoutput vector is arranged in the top-left M×2 (M×1) or 2×M (M×2) region,and for a region other than the top-left M×2 (M×1) or 2×M (M×2) regionin the partition block, all of them may be configured to be filled withzero values (zero-out) or to maintain the transform coefficientreconstructed through residual coding and dequantization processes as itis.

As in No. 3, when constructing the input vector, the input data may bearranged according to the scanning order of FIG. 18, and an input vectormay be constructed with the reduced number of input data (e.g., 8instead of 16) in order to adjust the computational complexity for theworst case to a certain level or less.

For example, when using 8 input data and when M=8, only the left 16×8matrix may be taken from the corresponding 16×16 matrix, and bemultiplied, thereby obtaining 16 output data. The complexity adjustmentfor the worst case will be described later.

While the above embodiment presents a case in which symmetry is appliedbetween an M×2 (M×1) block and a 2×M (1×M) block when applying LFNST,different LFNST sets may be applied to the two block shapes,respectively, according to another example.

Hereinafter, various examples of the LFNST set configuration for the ISPmode and the mapping method using the intra prediction mode will bedescribed.

In the case of ISP mode, the LFNST set configuration may be differentfrom that of the existing LFNST set. In other words, kernels differentfrom the existing LFNST kernels may be applied, and a mapping tabledifferent from the mapping table between the intra prediction mode indexapplied to the current VVC standard and the LFNST set may be applied.The mapping table applied to the current VVC standard may be shown inTable 2.

In Table 2, the preModeIntra value means an intra prediction mode valuechanged in consideration of the WAIP, and the lfnstTrSetIdx value is anindex value indicating a specific LFNST set. Each LFNST set isconfigured with two LFNST kernels.

When the ISP prediction mode is applied, and when both the horizontallength and the vertical length of each partition block are equal to orgreater than 4, the same kernels as the LFNST kernels applied in thecurrent VVC standard may be applied, and the mapping table may be alsoapplied as it is. Of course, it is also possible to apply a differentmapping table and different LFNST kernels from the current VVC standard.

When the ISP prediction mode is applied, and when the horizontal lengthor the vertical length of each partition block is less than 4, adifferent mapping table and different LFNST kernels from the current VVCstandard may be applied. Hereinafter, Tables 5 to 7 show mapping tablesbetween an intra prediction mode value (intra prediction mode valuechanged in consideration of the WAIP) and an LFNST set, which may beapplied to an M×2 (M×1) block or a 2×M (1×M) block.

TABLE 5 predModeIntra lfnstTrSetIdx predModeIntra < 0 1  0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 12 1 13 <= predModeIntra <=23 2 24 <= predModeIntra <= 34 3 35 <= predModeIntra <= 44 4 45 <=predModeIntra <= 55 5 56 <= predModeIntra <= 66 6 67 <= predModeIntra <=80 6 81 <= predModeIntra <= 83 0

TABLE 6 predModeIntra lfnstTrSetIdx predModeIntra < 0 1  0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 23 1 24 <= predModeIntra <=44 2 45 <= predModeIntra <= 66 3 67 <= predModeIntra <= 80 3 81 <=predModeIntra <= 83 0

TABLE 7 predModeIntra lfnstTrSetIdx predModeIntra < 0 1  0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 80 1 81 <= predModeIntra <=83 0

The first mapping table of Table 5 includes seven LFNST sets, and themapping table of Table 6 includes four LFNST sets, and the mapping tableof Table 7 includes two LFNST sets. As another example, when configuredwith one LFNST set, the lfnstTrSetIdx value may be fixed to 0 withrespect to the preModeIntra value.

Hereinafter, a method for maintaining the computational complexity forthe worst case when LFNST is applied to the ISP mode will be described.

In the case of ISP mode, in order to maintain the number ofmultiplications per sample (or per coefficient, or per position) at acertain value or less when LFNST is applied, the application of LFNSTmay be restricted. Depending on the size of the partition block, thenumber of multiplications per sample (or per coefficient, or perposition) may be maintained at 8 or less by applying LFNST as follows.

1. When both the horizontal length and the vertical length of thepartition block are equal to or greater than 4, the same method as thecalculation complexity adjustment method for the worst case for LFNST inthe current VVC standard may be applied.

That is, when the partition block is a 4×block, instead of a 16×16matrix, in the forward direction, an 8×16 matrix obtained by samplingthe top 8 rows from a 16×16 matrix may be applied, and in the backwarddirection, a 16×8 matrix obtained by sampling the left 8 columns from a16×16 matrix may be applied. Additionally, when the partition block isan 8×8 block, in the forward direction, instead of a 16×48 matrix, an8×48 matrix obtained by sampling the top 8 rows from a 16×48 matrix maybe applied, and in the backward direction, instead of a 48×16 matrix, a48×8 matrix obtained by sampling the left 8 columns from a 48×16 matrixmay be applied.

In the case of a 4×N or N×4 (N>4) block, when forward transform isperformed, 16 coefficients generated after applying a 16×16 matrix onlyto the top-left 4×4 block are arranged in the top-left 4×4 region, andthe other regions may be filled with 0 values. Additionally, whenperforming inverse transform, 16 coefficients located in the top-left4×4 block may be arranged in the scanning order to configure an inputvector, and then 16 output data may be generated by multiplying the16×16 matrix. The generated output data may be arranged in the top-left4×4 region, and the remaining regions except for the top-left 4×4 regionmay be filled with zeros.

In the case of an 8×N or N×8 (N>8) block, when the forwardtransformation is performed, 16 coefficients generated after applyingthe 16×48 matrix only to the ROI region in the top-left 8×8 block(remaining regions excluding the bottom-right 4×4 block from thetop-left 8×8 block) may be arranged in the top-left 4×4 area, and theother regions may be filled with 0 values. Additionally, when performinginverse transform, 16 coefficients located in the top-left 4×4 block maybe arranged in the scanning order to configure an input vector, and then48 output data may be generated by multiplying the 48×16 matrix. Thegenerated output data may be filled in the ROI region, and the otherregions may be filled with 0 values.

2. When the size of the partition block is N×2 or 2×N and the LFNST isapplied to the top-left M×2 or 2×M region (M≤N), a matrix to which thesampling has been applied according to the N value may be applied.

When M=8, for a partition block of N=8, that is, an 8×2 or 2×8 block, inthe case of forward transform, instead of a 16×16 matrix, an 8×16 matrixobtained by sampling top 8 rows from a 16×16 matrix may be applied, andin the case of the inverse transform, instead of a 16×16 matrix, a 16×8matrix obtained by sampling the left 8 columns from a 16×16 matrix maybe applied.

When N is greater than 8, in the case of forward transform, 16 outputdata generated after applying the 16×16 matrix to the top-left 8×2 or2×8 block may be arranged in the top-left 8×2 or 2×8 block, and theremaining regions may be filled with 0 values. When performing inversetransform, 16 coefficients located in the top-left 8×2 or 2×8 block maybe arranged in the scanning order to configure an input vector, and then16 output data may be generated by multiplying the 16×16 matrix. Thegenerated output data may be arranged in the top-left 8×2 or 2×8 block,and all the remaining regions may be filled with 0 values.

3. When the size of the partition block is N×1 or 1×N and the LFNST isapplied to the top-left M×1 or 1×M region (M≤N), a matrix to which thesampling has been applied according to the N value may be applied.

When M=16, for a partition block of N=16, that is, an 16×1 or 1×16block, in the case of forward transform, instead of a 16×16 matrix, an8×16 matrix obtained by sampling top 8 rows from a 16×16 matrix may beapplied, and in the case of the inverse transform, instead of a 16×16matrix, a 16×8 matrix obtained by sampling the left 8 columns from a16×16 matrix may be applied.

When N is greater than 16, in the case of forward transform, 16 outputdata generated after applying the 16×16 matrix to the top-left 16×1 or1×16 block may be arranged in the top-left 16×1 or 1×16 block, and theremaining regions may be filled with 0 values. When performing inversetransform, 16 coefficients located in the top-left 16×1 or 1×16 blockmay be arranged in the scanning order to configure an input vector, andthen 16 output data may be generated by multiplying the 16×16 matrix.The generated output data may be arranged in the top-left 16×1 or 1×16block, and all the remaining regions may be filled with 0 values.

As another example, in order to maintain the number of multiplicationsper sample (or per coefficient, or per position) at a certain value orless, the number of multiplications per sample (or per coefficient, orper position) based on the ISP coding unit size rather than the size ofthe ISP partition block may be maintained at 8 or less. If there is onlyone block among the ISP partition blocks, which satisfies the conditionunder which the LFNST is applied, the complexity calculation for theworst case of LFNST may be applied based on the corresponding codingunit size rather than the size of the partition block. For example, whena luma coding block for a certain coding unit is partitioned into 4partition blocks of 4×4 size and coded by the ISP, and when no non-zerotransform coefficient exists for two partition blocks among them, theother two partition blocks may be respectively set to generate 16transform coefficients instead of 8 (based on the encoder).

Hereinafter, a method of signaling the LFNST index in the case of theISP mode will be described.

As described above, the LFNST index may have values of 0, 1, and 2,where 0 indicates that the LFNST is not applied, and 1 and 2respectively indicate either one of two LFNST kernel matrices includedin the selected LFNST set. The LFNST is applied based on the LFNSTkernel matrix selected by the LFNST index. A method of transmitting theLFNST index in the current VVC standard will be described as follows.

1. An LFNST index may be transmitted once for each coding unit (CU), andin the case of a dual-tree, individual LFNST indexes may be signaled fora luma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value isinferred to be a default value of 0. The case where the LFNST indexvalue is inferred to be 0 is as follows.

A. In the case of a mode in which no transform is applied (e.g.,transform skip, BDPCM, lossless coding, etc.)

B. When the primary transform is not DCT-2 (DST7 or DCT8), that is, whenthe transform in the horizontal direction or the transform in thevertical direction is not DCT-2

C. When the horizontal length or vertical length for the luma block ofthe coding unit exceeds the size of the transformable maximum lumatransform, for example, when the size of the transformable maximum lumatransform is 64, and when the size for the luma block of the codingblock is equal to 128×16, the LFNST cannot be applied.

In the case of the dual tree, it is determined whether or not the sizeof the maximum luma transform is exceeded for each of the coding unitfor the luma component and the coding unit for the chroma component.That is, it is checked for the luma block whether or not the size of themaximum transformable luma transform is exceeded, and it is checked forthe chroma block whether or not the horizontal/vertical length of thecorresponding luma block for the color format and the size of themaximum transformable luma transform exceed the size are exceeded. Forexample, when the color format is 4:2:0, the horizontal/vertical lengthof the corresponding luma block is twice that of the correspondingchroma block, and the transform size of the corresponding luma block istwice that of the corresponding chroma block. As another example, whenthe color format is 4:4:4, the horizontal/vertical length and transformsize and of the corresponding luma block are the same as those of thecorresponding chroma block.

A 64-length transform or a 32-length transform may mean a transformapplied to width or height having a length of 64 or 32, respectively,and “transform size” may mean 64 or 32 as the corresponding length.

In the case of a single tree, after checking whether or not a horizontallength or a vertical length of a luma block exceeds the maximumtransformable luma transform block size, if it exceeds, the LFNST indexsignaling may be omitted.

D. The LFNST index may be transmitted only when both the horizontallength and the vertical length of the coding unit are equal to orgreater than 4.

In the case of a dual tree, the LFNST index may be signaled only whenboth the horizontal and vertical lengths for a corresponding component(i.e., a luma or chroma component) are equal to or greater than 4.

In the case of a single tree, the LFNST index may be signaled when boththe horizontal and vertical lengths for the luma component are equal toor greater than 4.

E. If the position of the last non-zero coefficient is not a DC position(top-left position of the block), and if the position of the lastnon-zero coefficient is not a DC position, in the case of a luma blockof a dual tree type, the LFNST index is transmitted. In the case of adual tree type chroma block, if any one of the position of the lastnon-zero coefficient for Cb and the position of the last non-zerocoefficient for Cr is not a DC position, the corresponding LNFST indexis transmitted.

In the case of the single tree type, if the position of the lastnon-zero coefficient of any one of the luma component, Cb component, andCr component is not the DC position, the LFNST index is transmitted.

Here, if a coded block flag (CBF) value indicating whether or not atransform coefficient for one transform block exists is 0, the positionof the last non-zero coefficient for the corresponding transform blockis not checked in order to determine whether or not the LFNST index issignaled. That is, when the corresponding CBF value is 0, since notransform is applied to the corresponding block, the position of thelast non-zero coefficient may not be considered when checking thecondition for the LFNST index signaling.

For example, 1) in the case of a dual tree type and a luma component, ifthe corresponding CBF value is 0, the LFNST index is not signaled, 2) inthe case of a dual tree type and chroma component, if the CBF value forCb is 0 and the CBF value for Cr is 1, only the position of the lastnon-zero coefficient for Cr is checked and the corresponding LFNST indexis transmitted, 3) in the case of a single tree type, the position ofthe last non-zero coefficient is checked only for components having aCBF value of 1 for each of luma, Cb, and Cr.

F. When it is confirmed that the transform coefficient exists at aposition other than a position where the LFNST transform coefficient mayexist, the LFNST index signaling may be omitted. In the case of a 4×4transform block and an 8×8 transform block, LFNST transform coefficientsmay exist at eight positions from the DC position according to thetransform coefficient scanning order in the VVC standard, and theremaining positions are filled with zeros. Additionally, when the 4×4transform block and the 8×8 transform block are not, LFNST transformcoefficients may exist in sixteen positions from the DC positionaccording to the transform coefficient scanning order in the VVCstandard, and the remaining positions are filled with zeros.

Accordingly, if the non-zero transform coefficients exists in the regionwhich should be filled with the zero value after progressing theresidual coding, the LFNST index signaling may be omitted.

Meanwhile, the ISP mode may also be applied only to the luma block, ormay be applied to both the luma block and the chroma block. As describedabove, when ISP prediction is applied, the corresponding coding unit maybe divided into two or four partition blocks and predicted, and atransform may be applied to each of the partition blocks. Therefore,also when determining a condition for signaling the LFNST index in unitsof coding units, it is necessary to take into consideration the factthat the LFNST may be applied to respective partition blocks. Inaddition, when the ISP prediction mode is applied only to a specificcomponent (e.g., a luma block), the LFNST index must be signaled inconsideration of the fact that only the component is divided intopartition blocks. The LFNST index signaling methods available in the ISPmode are summarized as follows.

1. An LFNST index may be transmitted once for each coding unit (CU), andin the case of a dual-tree, individual LFNST indexes may be signaled fora luma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value isinferred to be a default value of 0. The case where the LFNST indexvalue is inferred to be 0 is as follows.

A. In the case of a mode in which no transform is applied (e.g.,transform skip, BDPCM, lossless coding, etc.)

B. When the horizontal length or vertical length for the luma block ofthe coding unit exceeds the size of the transformable maximum lumatransform, for example, when the size of the transformable maximum lumatransform is 64, and when the size for the luma block of the codingblock is equal to 128×16, the LFNST cannot be applied.

Whether or not to signal the LFNST index may be determined based on thesize of the partition block instead of the coding unit. That is, if thehorizontal or vertical length of the partition block for thecorresponding luma block exceeds the size of the transformable maximumluma transformation, the LFNST index signaling may be omitted and theLFNST index value may be inferred to be 0.

In the case of the dual tree, it is determined whether or not the sizeof the maximum luma transform is exceeded for each of the coding unit orpartition block for the luma component and the coding unit or partitionblock for the chroma component. That is, if the horizontal and verticallengths of the coding unit or partition block for luma are compared withthe maximum luma transform size, respectively, and at least one of themis greater than the maximum luma transform size, the LFNST is notapplied, and in the case of a coding unit or partition block for chroma,the horizontal/vertical length of the corresponding luma block for thecolor format and the size of the maximum transformable luma transformare compared. For example, when the color format is 4:2:0, thehorizontal/vertical length of the corresponding luma block is twice thatof the corresponding chroma block, and the transform size of thecorresponding luma block is twice that of the corresponding chromablock. As another example, when the color format is 4:4:4, thehorizontal/vertical length and transform size and of the correspondingluma block are the same as those of the corresponding chroma block.

In the case of a single tree, after checking whether or not a horizontallength or a vertical length for a luma block (coding unit or partitionblock) exceeds the maximum transformable luma transform block size, ifit exceeds, the LFNST index signaling may be omitted.

C. If the LFNST included in the current VVC standard is applied, theLFNST index may be transmitted only when both the horizontal length andthe vertical length of the partition block are equal to or greater than4.

If the LFNST for the 2×M (1×M) or M×2 (M×1) block is applied in additionto the LFNST included in the current VVC standard, the LFNST index maybe transmitted only when the size of the partition block is equal to orlarger than a 2×M (1×M) or M×2 (M×1) block. Here, the expression “theP×Q block is equal to or greater than the R×S block” means that P≥R andQ≥S.

In summary, the LFNST index can be transmitted only when the partitionblock is equal to or greater than the minimum size to which the LFNST isapplicable. In the case of a dual tree, the LFNST index can be signaledonly when the partition block for the luma or chroma component is equalto or larger than the minimum size to which the LFNST is applicable. Inthe case of a single tree, the LFNST index can be signaled only when thepartition block for the luma component is equal to or larger than theminimum size to which LFNST is applicable.

In this document, the expression “the M×N block is greater than or equalto the K×L block” means that M is greater than or equal to K and N isgreater than or equal to L. The expression “the M×N block is larger thanthe K×L block” means that M is greater than or equal to K and N isgreater than or equal to L, and that M is greater than K or N is greaterthan L. The expression “the M×N block less than or equal to the K×Lblock” means that M is less than or equal to K and N is less than orequal to L, while the expression “the M×N block is smaller than the K×Lblock” means that M is less than or equal to K and N is less than orequal to L, and that M is less than K or N is less than L.

D. If the position of the last non-zero coefficient is not a DC position(top-left position of the block), and if the position of the lastnon-zero coefficient is not a DC position in any one of all partitionblocks In the case of a dual tree type luma block, the LFNST index istransmitted. In the case of a dual tree type and a chroma block, if atleast one of the position of the last non-zero coefficient of allpartition blocks for Cb (if the ISP mode is not applied to the chromacomponent, the number of partition blocks is considered to be one) andthe position of the last non-zero coefficient of all partition blocksfor Cr (if the ISP mode is not applied to the chroma component, thenumber of partition blocks is considered to be one) is not a DCposition, the corresponding LNFST index may be transmitted.

In the case of the single tree type, if the position of the lastnon-zero coefficient of any one of all partition blocks for the lumacomponent, the Cb component and the Cr component is not the DC position,the corresponding LFNST index may be transmitted.

Here, if the value of the coded block flag (CBF) indicating whether atransform coefficient exists for each partition block is 0, the positionof the last non-zero coefficient for the corresponding partition blockis not checked in order to determine whether or not the LFNST index issignaled. That is, when the corresponding CBF value is 0, since notransform is applied to the corresponding block, the position of thelast non-zero coefficient for the corresponding partition block is notconsidered when checking the condition for the LFNST index signaling.

For example, 1) in the case of a dual tree type and a luma component, ifthe corresponding CBF value for each partition block is 0, the partitionblock is excluded when determining whether or not to signal the LFNSTindex, 2) in the case of a dual tree type and a chroma component, if theCBF value for Cb is 0 and the CBF value for Cr is 1 for each partitionblock, only the position of the last non-zero coefficient for Cr ischecked to determine whether or not to signal the LFNST index, 3) in thecase of the single tree type, it is possible to determine whether or notto signal the LFNST index by checking the position of the last non-zerocoefficient only for blocks having a CBF value of 1 for all partitionblocks of the luma component, the Cb component, and the Cr component.

In the case of the ISP mode, image information may also be configured sothat the position of the last non-zero coefficient is not checked, andan embodiment thereof is as follows.

i. In the case of the ISP mode, the LFNST index signaling may be allowedwithout checking the position of the last non-zero coefficient for boththe luma block and the chroma block. That is, even if the position ofthe last non-zero coefficient for all partition blocks is the DCposition or the corresponding CBF value is 0, the LFNST index signalingmay be allowed.

ii. In the case of the ISP mode, the checking of the position of thelast non-zero coefficient only for the luma block may be omitted, and inthe case of the chroma block, the checking of the position of the lastnon-zero coefficient may be performed in the above-described manner. Forexample, in the case of a dual tree type and a luma block, the LFNSTindex signaling is allowed without checking the position of the lastnon-zero coefficient, and in the case of a dual tree type and a chromablock, whether or not a corresponding LFNST index is signaled may bedetermined by checking whether or not a DC position exists for theposition of the last non-zero coefficient in the above-described manner.

iii. In the case of the ISP mode and the single tree type, the i or iimethod may be applied. That is, in the case of the ISP mode and when thenumber i is applied to the single tree type, it is possible to omit thechecking of the position of the last non-zero coefficient for both theluma block and the chroma block and allow LFNST index signaling.Alternatively, by applying section ii, for the partition blocks for theluma component, the checking of the position of the last non-zerocoefficient is omitted, and for the partition blocks for the chromacomponent (if ISP is not applied for the chroma component, the number ofpartition blocks can be considered as 1), the position of the lastnon-zero coefficient is checked in the above-described manner, therebydetermining whether or not to signal the LFNST index.

E. When it is confirmed that the transform coefficient exists at aposition other than a position where the LFNST transform coefficient mayexist even for one partition block among all partition blocks, the LFNSTindex signaling may be omitted.

For example, in the case of a 4×4 partition block and an 8×8 partitionblock, LFNST transform coefficients may exist at eight positions fromthe DC position according to the transform coefficient scanning order inthe VVC standard, and the remaining positions are filled with zeros.Additionally, if it is equal to or greater than 4×4 and is not a 4×4partition block nor an 8×8 partition block, LFNST transform coefficientsmay exist at 16 positions from the DC position according to thetransform coefficient scanning order in the VVC standard, and all theremaining positions are filled with zeros.

Accordingly, if the non-zero transform coefficients exists in the regionwhich should be filled with the zero value after progressing theresidual coding, the LFNST index signaling may be omitted.

If the LFNST can be applied even when the partition block is 2×M (1×M)or M×2 (M×1), a region in which LFNST transform coefficients may belocated can be designated as follows. If a region other than the regionwhere the transform coefficients can be located may be filled with 0,and if a non-zero transform coefficient exists in the region that shouldbe filled with 0 when it is assumed that LFNST is applied, the LFNSTindex signaling may be omitted.

i. If the LFNST may be applied to a 2×M or M×2 block and M=8, only 8LFNST transform coefficients may be generated for a 2×8 or 8×2 partitionblock. When the transform coefficients are arranged in the scanningorder as shown in FIG. 18, 8 transform coefficients are arranged in thescanning order from the DC position, and the remaining 8 positions maybe filled with zeros.

For a 2×N or N×2 (N>8) partition block, 16 LFNST transform coefficientscan be generated, and when the transform coefficients are arranged inthe scanning order as shown in FIG. 18, 16 transform coefficients arearranged in the scanning order from the DC position, and the remainingregion may be filled with zeros. That is, in a 2×N or N×2 (N>8)partition block, a region other than the top-left 2×8 or 8×2 block maybe filled with zeros. Even for a 2×8 or 8×x2 partition block, 16transform coefficients may be generated instead of 8 LFNST transformcoefficients, and in this case, a region that must be filled with zerosdoes not occur. As described above, when the LFNST is applied, and whenit is detected that a non-zero transform coefficient exists in a regiondetermined to be filled with 0 in at least one partition block, LFNSTindex signaling may be omitted and the LFNST index may be inferred to be0.

ii. If the LFNST may be applied to a 1×M or M×1 block and M=16, only 8LFNST transform coefficients may be generated for a 1×16 or 16×1partition block. When the transform coefficients are arranged inleft-to-right or top-to-bottom scanning order, 8 transform coefficientsare arranged in the corresponding scanning order from the DC position,and the remaining 8 positions may be filled with zeros.

For a 1×N or N×1 (N>16) partition block, 16 LFNST transform coefficientscan be generated, and when the transform coefficients are arranged inleft-to-right or top-to-bottom scanning order, 16 transform coefficientsare arranged in the corresponding scanning order from the DC position,and the remaining region may be filled with zeros. That is, in a 1×N orN×1 (N>16) partition block, a region other than the top-left 1×16 or16×1 block may be filled with zeros.

Even for a 1x×16 or 16×1 partition block, 16 transform coefficients maybe generated instead of 8 LFNST transform coefficients, and in thiscase, a region that must be filled with zeros does not occur. Asdescribed above, when the LFNST is applied, and when it is detected thata non-zero transform coefficient exists in a region determined to befilled with 0 in at least one partition block, LFNST index signaling maybe omitted and the LFNST index may be inferred to be 0.

Meanwhile, in the case of the ISP mode, the length condition isindependently viewed for the horizontal direction and the verticaldirection, and DST-7 is applied instead of DCT-2 without signaling forthe MTS index. It is determined whether or not the horizontal orvertical length is greater than or equal to 4 and less than or equal to16, and a primary transform kernel is determined according to thedetermination result. Accordingly, in the case of the ISP mode, when theLFNST can be applied, the following transform combination configurationis possible.

1. When the LFNST index is 0 (including the case in which the LFNSTindex is inferred as 0), the primary transform decision condition at thetime of the ISP included in the current VVC standard may be followed. Inother words, it may be checked whether or not the length condition(being equal to or greater than 4 or equal to or less than 16) isindependently satisfied for the horizontal and vertical directions,respectively, and if it is satisfied, DST-7 may be applied instead ofDCT-2 for primary transform, while, if it is not satisfied, DCT-2 may beapplied.

2. For a case in which the LFNST index is greater than 0, the followingtwo configurations may be possible as a primary transform.

A. DCT-2 can be applied to both horizontal and vertical directions.

B. The primary transform decision condition at the time of the ISPincluded in the current VVC standard may be followed. In other words, itmay be checked whether or not the length condition (being equal to orgreater than 4 or equal to or less than 16) is independently satisfiedfor the horizontal and vertical directions, respectively, and if it issatisfied, DST-7 may be applied instead of DCT-2, while, if it is notsatisfied, DCT-2 may be applied.

In the ISP mode, image information may be configured such that the LFNSTindex is transmitted for each partition block rather than for eachcoding unit. In this case, in the above-described LFNST index signalingmethod, it may be regarded that only one partition block exists in aunit in which the LFNST index is transmitted, and it may be determinedwhether or not to signal the LFNST index.

Meanwhile, the signaling order of the LFNST index and the MTS index willbe described below.

According to an example, the LFNST index signaled in residual coding maybe coded after the coding position for the last non-zero coefficientposition, and the MTS index may be coded immediately after the LFNSTindex. In the case of this configuration, the LFNST index may besignaled for each transform unit. Alternatively, even if not signaled inresidual coding, the LFNST index may be coded after the coding for thelast significant coefficient position, and the MTS index may be codedafter the LFNST index.

The syntax of residual coding according to an example is as follows.

TABLE 8   residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) {  if ( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6 )       &&cIdx = = 0 && log2TbWidh > 4 )   log2ZoTWidth = 4  else   log2ZoTbWidth= Min( log2TbWith, 5 )  MaxCcbs = 2 * ( 1 << log2TbWith ) * ( 1<<log2TbHeight )  if( ( cu_sbt_flag && log2TbWidth < 6 && log2TbHeight < 6)       && cIdx = 0 && log2TbHeight > 4 )   log2ZoTbHeight = 4  else  log2ZoTbHeight = Min( log2TbHeight, 5 )  if( log2TbWidth > 0 )  last_sig_coeff_x_prefix  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix  remBinsPass1 = ( ( 1 << ( log2TbWidth +log2TbHeight ) ) * 7 ) >> 2  log2Sbw = ( Min( log2Width, log2TbHeight )< 2  ?  1  :  2 )  log2SbH = logSbW  if( log2TbWidth + log2TbHeight > 3) {    if( logt2bWidth < 2 ) {      log2SbW = log2TbWidth    log2SbH = 4− log2SbW   } else if( log2TbHeight < 2 ) {    log2SbH = log2TbHeight   log2SbW = 4 − log2SbH   }  }  numSbCoeff = 1 << ( log2SbW + log2SbH ) lastScanPos = numSbCoeff  lastSubBlock = ( 1 << ( log2TbWidth +log2TbHeight − ( log2SbW + log2SbH ) ) ) − 1  do {    if( lastScanPos == 0 ) {    lastScanPos = numSbCoeff    lastSubBlock− −   }  lastScanPos− −   xS = DiagScanOrder[ log2TbWidth − log2SbW ][log2TbHeight − log2SbH ]          [ lastSubBlock ][ 0 ]   yS =DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH ]         [ lastSubBlock ][ 1 ]   xC = ( xS << log2SbW ) + DiagScanOrder[log2SbW ][ log2SbH ][ lastScanPos ][ 0 ]   xC = ( yS << log2SbW ) +DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 1 ]  } while( ( xC !=  LastSignificantCoeffX )  ||  ( yC  !=  LastSignificantCoeffY ) )  cbWidth = CbWidth[ 0 ][ x0 ][ y0 ]   cbHeight = CbHeight[ 0 ][ x0 ][y0 ]  if( Mint( log2TbWidth, log2TbHeight )  >=  2 &&sps_lfnst_enabled_flag  = =  1 &&   CuPredModel[ chType ][ x0][ y0 ] = =MODE_INTRA &&   IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT &&  ( !intra_mip_flag[ x0 ][ y0 ]  ||  Min( log2TbWidth, log2TbHeight ) >=  4 )  &&   Max( cbWidth, cbHeight )  <=  MaxTbSizeY &&      ( cIdx == 0 || ( treeType = = DUAL_TREE_CHROMA &&      ( cIdx = = 1 || tu_cbf_cb[ x0 ][ y0 ] == 0 ) ) ) ) {   if( lastSubBlock = = 0 &&lastScanPos > 0 &&        !( lastScanPos > 7 && ( log2TbWidth = = 2 ||log2TbWidth = = 3 )        && log2TbWidth = = log2TbHeight ) )   lfnst_idx[ x0 ][ y0 ]  }  if( cIdx = = 0 && lfnst_idx[ x0 ][ y0 ] = =0 &&   ( log2TbWidth <= 5 ) && ( log2TbHeight <= 5 ) &&   (LastSignificantCoeffX < 16 ) && ( LastSignificantCoeffY < 16 ) &&   (IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT ) && ( !cu_sbt_flag) ) {   if( ( ( CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER &&   sps_explicit_mts_inter_enabled_flag )    ||( CuPredMode[ chType ][ x0][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )   tu_mts_idx[ x0 ][ y0 ]  }  if( tu_mts_idx[ x0 ][ y0 ] > 0 && cIdx = =0 && log2TbWidth > 4 )   log2ZoTbWidth = 4  if( tu_mts_idx[ x0 ][ y0 ] >0 && cIdx = = 0 && log2TbHeight > 4 )   log2ZoTbHeight = 4  log2TbWidth= log2ZoTbWidth  log2TbHeight = log2ZoTbHeight   ...

The meanings of the major variables shown in Table 8 are as follows.

1. cbWidth, cbHeight: the width and height of the current coding block

2. log2TbWidth, log2TbHeight: the log value of base-2 for the width andheight of the current transform block, it may be reduced, by reflectingthe zero-out, to a top-left region in which a non-zero coefficient mayexist.

3. sps_lfnst_enabled_flag: a flag indicating whether or not the LFNST isenabled, if the flag value is 0, it indicates that the LFNST is notenabled, and if the flag value is 1, it indicates that the LFNST isenabled. It is defined in the sequence parameter set (SPS).

4. CuPredMode[chType][x0][y0]: a prediction mode corresponding to thevariable chType and the (x0, y0) position, chType may have values of 0and 1, wherein 0 indicates a luma component and 1 indicates a chromacomponent. The (x0, y0) position indicates a position on the picture,and MODE_INTRA (intra prediction) and MODE_INTER (inter prediction) arepossible as a value of CuPredMode[chType][x0][y0].

5. IntraSubPartitionsSplit[x0][y0]: the contents of the (x0, y0)position are the same as in No. 4. It indicates which ISP partition atthe (x0, y0) position is applied, ISP_NO_SPLIT indicates that the codingunit corresponding to the (x0, y0) position is not divided intopartition blocks.

6. intra_mip_flag[x0][y0]: the contents of the (x0, y0) position are thesame as in No. 4 above. The intra_mip_flag is a flag indicating whetheror not a matrix-based intra prediction (MIP) prediction mode is applied.If the flag value is 0, it indicates that MIP is not enabled, and if theflag value is 1, it indicates that MIP is enabled.

7. cIdx: the value of 0 indicates luma, and the values of 1 and 2indicate Cb and Cr which are respectively chroma components.

8. treeType: indicates single-tree and dual-tree, etc. (SINGLE_TREE:single tree, DUAL_TREE_LUMA: dual tree for luma component,DUAL_TREE_CHROMA: dual tree for chroma component)

9. tu_cbf_cb[x0][y0]: the contents of the (x0, y0) position are the sameas in No. 4. It indicates the coded block flag (CBF) for the Cbcomponent. If its value is 0, it means that no non-zero coefficients arepresent in the corresponding transform unit for the Cb component, and ifits value is 1, it indicates that non-zero coefficients are present inthe corresponding transform unit for the Cb component.

10. lastSubBlock: It indicates a position in the scan order of asub-block (Coefficient Group (CG)) in which the last non-zerocoefficient is located. 0 indicates a sub-block in which the DCcomponent is included, and in the case of being greater than 0, it isnot a sub-block in which the DC component is included.

11. lastScanPos: It indicates the position where the last significantcoefficient is in the scan order within one sub-block. If one sub-blockincludes 16 positions, values from 0 to 15 are possible.

12. lfnst_idx[x0][y0]: LFNST index syntax element to be parsed. If it isnot parsed, it is inferred as a value of 0. That is, the default valueis set to 0, indicating that LFNST is not applied.

13. LastSignificantCoeffX, LastSignificantCoeffY: They indicate the xand y coordinates where the last significant coefficient is located inthe transform block. The x-coordinate starts at 0 and increases fromleft to right, and the y-coordinate starts at 0 and increases from topto bottom. If the values of both variables are 0, it means that the lastsignificant coefficient is located at DC.

14. cu_sbt_flag: A flag indicating whether or not SubBlock Transform(SBT) included in the current VVC standard is enabled. If a flag valueis 0, it indicates that SBT is not enabled, and if the flag value is 1,it indicates that SBT is enabled.

15. sps_explicit_mts_inter_enabled_flag,sps_explicit_mts_intra_enabled_flag: Flags indicating whether or notexplicit MTS is applied to inter CU and intra CU, respectively. If acorresponding flag value is 0, it indicates that MTS is not enabled toan inter CU or an intra CU, and if the corresponding flag value is 1, itindicates that MTS is enabled.

16. tu_mts_idx[x0][y0]: MTS index syntax element to be parsed. If it isnot parsed, it is inferred as a value of 0. That is, the default valueis set to 0, indicating that DCT-2 is enabled to both the horizontal andvertical directions.

As shown in Table 8, in the case of a single tree, it is possible todetermine whether or not to signal the LFNST index using only the lastsignificant coefficient position condition for luma. That is, if theposition of the last significant coefficient is not DC and the lastsignificant coefficient exists in the top-left sub-block (CG), forexample, a 4×4 block, then the LFNST index is signaled. In this case, inthe case of the 4×4 transform block and the 8×8 transform block, theLFNST index is signaled only when the last significant coefficientexists at positions 0 to 7 in the top-left sub-block.

In the case of the dual tree, the LFNST index is signaled independentlyof each of luma and chroma, and in the case of chroma, the LFNST indexcan be signaled by applying the last significant coefficient positioncondition only to the Cb component. The corresponding condition may notbe checked for the Cr component, and if the CBF value for Cb is 0, theLFNST index may be signaled by applying the last significant coefficientposition condition to the Cr component.

‘Min(log2TbWidth, log2TbHeight)>=2’ of Table 8 may be expressed as“Min(tbWidth, tbHeight)>=4”, and ‘Min(log2TbWidth, log2TbHeight)>=4’ maybe expressed as “Min(tbWidth, tbHeight)>=16”.

In Table 8, log2ZoTbWidth and log2ZoTbHeight mean log values whose widthand height base are 2 (base-2) for the top-left region where the lastsignificant coefficient may exist by zero-out, respectively.

As shown in Table 8, log2ZoTbWidth and log2ZoTbHeight values may beupdated in two places. The first is before the MTS index or LFNST indexvalue is parsed, and the second is after the MTS index is parsed.

The first update is before the MTS index (tu_mts_idx[x0][y0]) value isparsed, so log2ZoTbWidth and log2ZoTbHeight can be set regardless of theMTS index value.

After the MTS index is parsed, log2ZoTbWidth and log2ZoTbHeight are setwhen the MTS index value is greater than 0 (in the case of DST-7/DCT-8combination). When DST-7/DCT-8 is independently applied to each of thehorizontal direction and the vertical direction in the primarytransform, there may be up to 16 significant coefficients per row orcolumn for each direction. That is, after applying DST-7/DCT-8 with alength of 32 or more, up to 16 transform coefficients can be derivedfrom the left or top. Accordingly, for a 2D block, when DST-7/DCT-8 isapplied to both the horizontal and vertical directions, the effectivecoefficient can exist only up to the top-left 16×16 region.

Additionally, when DCT-2 is independently applied to each of thehorizontal direction and the vertical direction in the primarytransform, there may be up to 32 significant coefficients per row orcolumn for each direction. That is, when applying DCT-2 with a length of64 or more, up to 32 transform coefficients can be derived from the leftor top. Accordingly, for a 2D block, when DCT-2 is applied to both thehorizontal and vertical directions, the effective coefficient can existonly up to the top-left 32×32 region.

In addition, when DST-7/DCT-8 is applied on one side, and DCT-2 isapplied on the other side to horizontal and vertical directions, 16significant coefficients may exist in the former direction, and 32significant coefficients may exist in the latter direction. For example,in the case of a 64×8 transform block, if DCT-2 is applied in thehorizontal direction and DST-7 is applied in the vertical direction (itmay occur in a situation where implicit MTS is applied), a significantcoefficient may exist in up to a top-left 32×8 region.

If, as shown in Table 8, log2ZoTbWidth and log2ZoTbHeight are updated intwo places, that is, before MTS index parsing, the ranges oflast_sig_coeff_x_prefix and last_sig_coeff_y_prefix may be determined bylog2ZoTbWidth and log2ZoTbHeight as shown in the table below.

TABLE 9 7.4.9.11  Residual coding semantics   ......last_sig_coeff_x_prefix specifies the prefix of the column position ofthe last significant coefficient in scanning order within a transformblock. The values of last_sig_coeff_x_prefix shall be is the range of 0to ( log2ZoTbWidth << 1 ) − 1. inclusive. When last_sig_coeff_x_prefixis not present, it is inferred to be 0. last_sig_coeff_y_prefixspecifies the prefix of the row position of the last significantcoefficient in scanning order within a transform block. The values oflast_sig_coeff_y_prefix shall be in the range of 0 to ( log2ZoTbHeight<< 1 ) − 1. inclusive. When last_sig_coeff_y_prefix is not present, itis inferred to be 0. ......

Additionally, in this case, the maximum values oflast_sig_coeff_x_prefix and last_sig_coeff_y_prefix may be set byreflecting log2ZoTbWidth and log2TbHeight values in the binarizationprocess for last_sig_coeff_x_prefix and last_sig_coeff_y_prefix.

TABLE 10 Table 9-77-Syntax elements and associated binarizationsresidual last_sig_coeff_x_prefix TR cMax = (log2ZoTbWidth << 1) − 1,cRiceParam = 0 coding last_sig_coeff_y_prefix TR cMax = (log2ZoTbHeight<< 1) − 1, cRiceParam = 0 ( ) last_sig_coeff_x_suffix FL cMax = (1 <<((last_sig_coeff_x_prefix >> 1) − 1) − 1) last_sig_coeff_y_suffix FLcMax = (1 << (last_sig_coeff_y_prefix >> 1) − 1) − 1) . . . . . . . . .

If, when coding the last significant coefficient, log2ZoTbWidth andlog2ZoTbHeight are not considered, and log2ZoTbWidth and log2ZoTbHeightare updated after coding the LFNST index and the MTS index, thespecification text of residual coding may be as shown in the tablebelow. Description of each syntax of Table 11 is the same as that ofTable 8.

TABLE 11   residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) { if( log2TbWidth > 0 )   last_sig_coeff_x_prefix  if log2TbHeight > 0 )  last_sig_coeff_y_prefix  if last_sig coeff_x_prefix > 3 )  last_sig_coeff_x_suffix  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix  ......   cbWidth = CbWidth[ 0 ][ x0 ][ y0 ]  cbHeight = CbHeight[ 0 ][ x0 ][ y0 ]  if( Min( log2TbWidtb,log2TbWeight ) >= 2 && sps_lfnst_enabled_flag = = 1 &&   CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&   IntraSubPartitionsSplit[ x0 ][y0 ] = = ISP_NO_SPLIT &&   ( !intra_mip_flag[ x0 ][ y0 ] || Min(log2TbWidth, log2TbHeitgh ) > 4 ) &&   Max( cbWidth, cbHeight ) <=MaxTbSizeY &&      ( cIdx = = 0 || ( treeType = = DUAL_TREE_CHROMA &&     ( cIdx = = 0 ||  tu_cbf_cb[ x0 ][ y0 ] == 0 ) ) ) ) {   if(lastSubBlock = = 0 && lastScanPos > 0 &&       !( lastScanPos > 7 && (log2TbWidth = = 2 || log2TbWidth = = 3 )       && log2TbWidth = =log2TbHeight ) )    lfst_idx[ x0 ][ y0 ]  }  if( cIdx = = 0 &&lfnst_idx[ x0 ][ y0 ] = = 0 &&   ( log2TbWidth <= 5 ) && ( log2TbHeight<= 5 ) &&   ( LasSignificantCoeffX < 16 ) && ( LastSignificanCoeffY < 16) &&   ( IntraSubPartitionsSplit[ x ][ y0 ] = = ISP_NO_SPLIT ) && (!cu_sbt_flag ) ) {   if( ( CuPredMode[ chType ][ x0 ][ y0 ] MODE_INTER&&    sps_explicit_mts_inter_enabled_flag )    || ( CuPredMode[ chType][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag )) )    tu_mts_idx[ x0 ][ y0 ]  }  if( ( tu_mts_idx[ x0 ][ y0 ] > 0 ||  ( cu_sbt_flag && log2TbWidth < 6 && log2TbHleight < 6 ) )    && cIdx == 0 && log2TbWidth > 4 )   log2ZoTbWidth = 4  else   logZoTbWidth = Min(log2TbWidth, 5 )  MaxCcbs = 2 * ( 1 << log2TbWidth) * ( 1<< log2TbHeight)  if( tu_mts__idx[ x0 ][ y0 ] > 0 ||   ( cu_sbt_flag && log2TbWidth < 6&& log2TbHeight < 6 ) )    && cIdx = = 0 && log2TbHeight > 4 )  logZoTbHeight = 4  else   log2ZoTbHeight = Min( log2TbHeight, 5 ) log2TbWidth = log2ZoTbWidth  log2TbHeight = log2ZoTbHeight   ...

According to Table 11, the ranges of last_sig_coeff_x_prefix andlast_sig_coeff_y_prefix constituting the last significant coefficientposition coding may be set based on log2TbWidth and log2TbHeight asshown in Table 12, and in this case, binarization may also be performedbased on log2TbWidth and log2TbHeight (Table 13).

TABLE 12   7.4.9.11  Residual coding semantics ......last_sig_coeff_x_prefix specifies the prefix of the column position ofthe last significant coefficient in scanning order within a transformblock. The values of last_sig_coeff_x_prefix shall be in the range of 0to ( log2TbWidth << 1 ) − 1, inclusive. When last_sig_coeff_x_prefix isnot present, it is inferred to be 0. last_sig_coeff_y_prefix specifiesthe prefix of the row position of the last significant coefficient inscanning order within a transform block. The values oflast_sig_coeff_y_prefix shall be in the range of 0 to ( log2TbHeigh << 1) − 1, inclusive.

TABLE 13 Table 9-77-Syntax elements and associated binarizationsresidual last_sig_coeff_x_prefix TR cMax = (log2TbWidth << 1) − 1,cRiceParam = 0 coding last_sig_coeff_y_prefix TR cMax = (log2TbHeight<< 1) − 1, cRiceParam = 0 ( ) last_sig_coeff_x_suffix FL cMax = (1 <<((last_sig_coeff_x_prefix >> 1) − 1) − 1) last_sig_coeff_y_suffix FLcMax = (1 << ((last_sig_coeff_y_prefix >> 1) − 1) − 1) . . . . . . . . .

Meanwhile, according to an example, in the case of the ISP mode, whenthe LFNST is applied, and when the signaling of Table 8 is applied, thespecification text may be configured as shown in Table 14. When comparedwith Table 8, the condition (IntraSubPartitionsSplit[x0][y0]==ISP_NO_SPLIT in Table 8) for signaling the LFNST index only for casesother than the ISP mode has been deleted.

In the case of a single tree, if the MTS index transmitted at the timeof lume (cIdx=0) is reused at the time of chroma, the LFNST index thathas been transmitted to the first ISP partition block in which thesignificant coefficient exists can be applied to the chroma transformblock. Alternatively, even in the case of a single tree, for the chromacomponent, the LFNST index may be signaled separately from the lumacomponent. Descriptions of the variables in Table 14 are the same asthose of Table 8.

TABLE 14   residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) { ...   tbWidth = 1 << log2TbWidth   tbHeight = 1 << log2TbHeight   ... if( log2TbWidth > 0 )   last_sig_coeff_x_prefix  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix ...     cbWidth = CbWidth[ 0 ][ x0 ][ y0 ]    cbHeight = CbHeight[ 0 ][ x0 ][ y0 ]  if( Min( log2TbWidth.log2TbHeight ) >= 2 && sps_lfnst_enabled_flag = = 1 &&   CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&   ( !intra_mip_flag[ x0 ][ y0 ]|| Min( log2TbWidth, log2TbHeight ) >= 4 ) &&   Max( cbWidth, cbHeight )<= MaxTbSizeY &&       ( cIdx = = 0 || ( treeType = = DUAL_TREE_CHROMA&&       ( cIdx = = 1 ||   tu_cbf_cb[ x0 ][ y0 ] == 0 ) ) ) {    if(lastSubBlock = = 0 && lastScanPos > 0 &&         !( lastScanPos > 7 && (log2TbWidth = = 2 || log2TbWidth = = 3 )           && log2TbWidth = =log2TbHeight ) )     lfnts_idx[ x0 ][ y0 ]   }   if( cIdx = = 0 &&lfnst_idx[ x0 ][ y0 ] = = 0 &&    ( tbWidth <= 32 ) && ( tbHeight <= 32) &&    ( LastSignificantCoeffX < 16 ) && ( LastSignificantCoeffY < 16 )&&    ( IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT ) && (!cu_sbt_flag ) ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ] = =MODE_INTER &&     sps_explicit_mts_inter_enabled_flag )     || (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     tu_mts_idx[ x0 ][ y0 ]  } ...

According to another example, in the case of the ISP in Table 14, if thelast significant coefficient is allowed to be located in the DCposition, the parsing condition of the LFNST index may be changed asfollows.

TABLE 15   ...   if( Min( log2TbWidth, log2TbHeight )  >=  2  &&sps_lfnst_enabled_flag  = =  1 &&    CuPredMode[ chType ][ x0 ][ y0 ]  ==  MODE_INTRA &&    ( !intra_mip_flag[ x0 ][ y0 ]   ||  Min(log2TbWidth, log2TbHeight )  >=  4 )  &&    Max( cbWidth, cbHeight ) <=  MaxTbSizeY &&       ( cIdx = = 0 || ( treeType = = DUAL_TREE_CHROMA&&       ( cIdx = = 1 ||   tu_cbf_cb[ x0 ][ y0 ] == 0 ) ) ) {    if(lastSubBlock  = =  0 && ( lastScanPos > 0 ||    IntraSubPartitionsSplit[ x0 ][ y0 ] != ISP_NO_SPLIT ) &&     !(lastScanPos > 7 && ( log2TbWidth = = 2  ||  log2TbWidth = = 3 )     &&log2TbWidth = = log2TbHeight ) )      lfnst_idx[ x0 ][ y0 ]   } ...

‘Min(log2TbWidth, log2TbHeight)>=2’ of Tables 14 and 15 may be expressedas “Min(tbWidth, tbHeight)>=4”, and ‘Min(log2TbWidth, log2TbHeight)>=4’may be expressed as “Min(tbWidth, tbHeight)>=16”.

As described above, even in the case of a single tree, for the chromacomponent, when the corresponding LFNST index is transmitted separatelyfrom the luma component, the lfsnt_idx parsing condition may be changedas follows.

TABLE 16     if( Min( log2TbWidth, log2TbHeight )  >=  2  && sps_lfnst_enabled_flag  = =  1 &&    CuPredMode[ chType ][ x ][ y0 ]  ==  MODE_INTRA &&    ( !intra_mip_flag[ x0 ][ y0 ]   ||  Min(log2TbWidth, log2TbHeight )  >=  4 )  &&    Max( cbWidth, cbHeight ) <=MaxTbSizeY &&       ( cIdx = = 0 || ( cIdx = = 1  ||  tu_cbf_cb[ x0 ][y0 ] == 0 ) ) ) {    if( lastSubBlock = = 0 && lastScanPos > 0 &&        !( lastScanPos > 7 && ( log2TbWidth = = 2  ||  log2TbWidth = = 3)           && log2TbWidth = = log2TbHeight ) )     lfnst_idx[ x0 ][ y0]   }

The following drawings were prepared to explain a specific example ofthe present specification. Since the names of specific devices describedin the drawings or the names of specific signals/messages/fields arepresented by way of example, the technical features of the presentspecification are not limited to the specific names used in thefollowing drawings.

FIG. 19 is a flowchart showing operation of a video decoding apparatusaccording to an embodiment of the present document.

Each step disclosed in FIG. 19 is based on some of the contentsdescribed above in FIGS. 2 to 18. Therefore, an explanation for thespecific content duplicated with contents described above in FIGS. 2 to19 will be omitted or made briefly.

The decoding apparatus 200 according to an embodiment may receiveresidual information from the bitstream (S1910).

More specifically, the decoding apparatus 200 may decode information onquantized transform coefficients for the current block from thebitstream, and may derive the quantized transform coefficients for thetarget block based on the information on the quantized transformcoefficients for the current block. The information on the quantizedtransform coefficients for the target block may be incorporated in asequence parameter set (SPS) or a slice header, and may include at leastone of information on whether or not the reduced transform (RST) isapplied, information on the reduced factor, information on a minimumtransform size to which the reduced transform is applied, information ona maximum transform size to which the reduced transform is applied, andInformation on the transform index indicating any one of the simplifiedinverse transform size and transform kernel matrix included in thetransform set.

In addition, the decoding apparatus may further receive information onthe intra prediction mode for the current block and information onwhether or not the ISP is applied to the current block. The decodingapparatus may derive whether or not the current block is divided into apredetermined number of sub-partition transform blocks by receiving andparsing flag information indicating whether or not to apply ISP codingor ISP mode. Here, the current block may be a coding block.Additionally, the decoding apparatus may derive the size and number ofdivided sub-partition blocks through flag information indicating inwhich direction the current block will be divided.

The decoding apparatus 200 may derive transform coefficients byperforming dequantization on residual information on the current block,that is, quantized transform coefficients (S1920).

The derived transform coefficients may be arranged according to thereverse diagonal scan order in units of 4×4 blocks, and transformcoefficients within the 4×4 block may also be arranged according to thereverse diagonal scan order. That is, transform coefficients on whichdequantization has been performed may be arranged according to a reversescan order applied in a video codec such as in VVC or HEVC.

A transform coefficient derived based on this residual information maybe a dequantized transform coefficient as described above, and may alsobe a quantized transform coefficient. That is, the transform coefficientmay be any data capable of checking whether or not it is non-zero datain the current block regardless of whether or not it is quantized.

The decoding apparatus may derive residual samples by applying aninverse transform to the quantized transform coefficients.

As described above, the decoding apparatus may derive residual samplesby applying LFNST, which is a non-separable transform, or MTS, which isa separable transform, and such transforms may be performed based on theLFNST index indicating the LFNST kernel, that is, the LFNST matrix, andthe MTS index indicating the MTS kernel, respectively.

The decoding apparatus may receive and parse the LFNST index or the MTSindex at the residual coding level or the coding unit level, accordingto an example.

According to an example, the LFNST index indicating the LFNST kernel maybe parsed before the MTS index indicating the MTS kernel (S1930).

The MTS index may be parsed after the LFNST index, and the MTS index maybe parsed according to a specific condition of the LFNST index.

Meanwhile, the residual coding level may include a syntax for the lastsignificant coefficient position information, and the LFNST index may beparsed after the last significant coefficient position information isparsed.

According to an example, when the current block is a luma block and theLFNST index is 0, the MTS index may be parsed. That is, when the currentblock is a luma block, and if the LFNST index is greater than 0, the MTSindex may not be parsed.

According to an example, when the tree type of the current block is adual tree, the LFNST index for each of the luma block and the chromablock may be parsed.

Meanwhile, in the deriving the transform coefficient, the width andheight for the top-left region in which the last significant coefficientmay exist in the current block by zero-out may be derived, and the widthand height for the top-left region may be derived before parsing the MTSindex.

Meanwhile, the position of the last significant coefficient may bederived by the width and height for the top-left region, and the lastsignificant coefficient position information may be binarized based onthe width and height for the top-left region.

The decoding apparatus may derive a residual sample by applying at leastone of LFNST performed based on the LFNST index, and MTS performed basedon the MTS index (S1940).

Subsequently, the decoding apparatus 200 may generate reconstructedpicture based on residual samples for the current block and predictionsamples for the current block (S1950).

The following drawings were prepared to explain a specific example ofthe present specification. Since the names of specific devices describedin the drawings or the names of specific signals/messages/fields arepresented by way of example, the technical features of the presentspecification are not limited to the specific names used in thefollowing drawings.

FIG. 20 is a flowchart showing operation of a video encoding apparatusaccording to an embodiment of the present document.

Each step disclosed in FIG. 20 is based on some of the contentsdescribed above in FIGS. 3 to 18. Therefore, an explanation for thespecific content duplicated with contents described above in FIGS. 1,and 3 to 18 will be omitted or made briefly.

The encoding apparatus 100 according to an embodiment may derive theprediction sample for the current block based on the intra predictionmode applied to the current block (S2010).

The encoding apparatus may perform prediction for each sub-partitiontransform block in the case where the ISP is applied to the currentblock.

The encoding apparatus may determine whether or not to apply the ISPcoding or ISP mode to the current block, that is, the coding block, andaccording to the determination result, it is possible to determine inwhich direction the current block is to be divided, and to derive thesize and number of sub-blocks to be divided.

The encoding apparatus 100 may derive residual samples for the currentblock based on the prediction samples (S2020).

Additionally, the encoding apparatus 100 may derive transformcoefficients for the current block by applying at least one of LFNST andMTS for the residual sample (S2030).

The primary transform may be performed through a plurality of transformkernels such as MTS, and in this case, the transform kernel may beselected based on the intra prediction mode.

Also, the encoding apparatus 100 may determine whether or not to performquadratic transform, or non-separable transform, specifically LFNST, ontransform coefficients for the current block, and may apply LFNST totransform coefficients to derive modified transform coefficients.

The LFNST is a non-separable transform that applies the transformwithout separating the coefficients in a specific direction, unlike theprimary transform that separates and transforms in a vertical orhorizontal direction, coefficients which are transform targets. Suchnon-separable transform may be a low-frequency non-separable transformthat applies transform only to a low-frequency region rather than theentire target block which is a transform target.

When the ISP is applied to the current block, the encoding apparatus maydetermine whether or not the LFNST can be applied to the height andwidth of the divided sub-partition block.

The encoding apparatus may determine whether or not the LFNST can beapplied to the height and width of the divided sub-partition block. Inthis case, the decoding apparatus may parse the LFNST index when theheight and width of the sub-partition block are equal to or greater than4.

The encoding apparatus may encode at least one of the LFNST indexindicating the LFNST kernel and the MTS index indicating the MTS kernel(S2040).

Meanwhile, the residual information may include the last significantcoefficient position information, and the LFNST index may be signaledafter the last significant coefficient position information.

According to an example, when the current block is a luma block and theLFNST index indicates 0, the encoding apparatus may encode the MTSindex.

According to an example, when the tree type of the current block is adual tree, the encoding apparatus may encode the LFNST index for each ofthe luma block and the chroma block.

According to an example, when the transform coefficient is derived, theencoding apparatus may derive the width and height for the top-leftregion in which the last significant coefficient may exist in thecurrent block by zero-out may derive the last significant coefficientposition based on the width and height for the top-left region, and maybinarize the last significant coefficient position information.

According to an example, the width and height for the top-left regionmay be derived before signaling of the MTS index.

In an example, the position of the last significant coefficient may bederived by the width and height for the top-left region according toTable 9, and the position information of the last significantcoefficient may be binarized based on the width and height for thetop-left region according to Table 10.

In this way, the encoding apparatus may configure image information sothat the LFNST index is signaled before the MTS index, and may output it(S2050).

Additionally, the encoding apparatus may derive the quantized transformcoefficients by performing quantization based on the transformcoefficient or modified transform coefficients for the current block,and may encode and output image information including information on thequantized transform coefficients.

The encoding apparatus may generate residual information includinginformation on quantized transform coefficients. The residualinformation may include the above-described transform relatedinformation/syntax element. The encoding apparatus may encodeimage/video information including the residual information, and mayoutput the encoded image/video information in the form of a bitstream.

More specifically, the encoding apparatus may generate information onthe quantized transform coefficients, and may encode information on thegenerated quantized transform coefficients.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

In addition, in the present disclosure, a quantized transformcoefficient and a transform coefficient may be referred to as atransform coefficient and a scaled transform coefficient, respectively.In this case, residual information may include information on atransform coefficient(s), and the information on the transformcoefficient(s) may be signaled through a residual coding syntax.Transform coefficients may be derived based on the residual information(or information on the transform coefficient(s)), and scaled transformcoefficients may be derived through inverse transform (scaling) of thetransform coefficients. Residual samples may be derived based on theinverse transform (transform) of the scaled transform coefficients.These details may also be applied/expressed in other parts of thepresent disclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

FIG. 21 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 21, the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming The digital storage medium may include various storage mediumssuch as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 22 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcorder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcorder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

1.-13. (canceled).
 14. An image decoding method performed by a decodingapparatus, the method comprising: receiving residual information from abitstream; deriving prediction samples for a current block; derivingtransform coefficients for the current block based on the residualinformation; deriving residual samples by applying at least one of LFNSTand MTS to the transform coefficients; and generating a reconstructedpicture based on the prediction samples and the residual samples,wherein the LFNST is performed based on an LFNST kernel related to anLFNST index; wherein the MTS is performed based on an MTS kernel relatedto an MTS index; wherein the LFNST index is parsed before the MTS index,and wherein the MTS index is signaled based on a value of the LFNSTindex.
 15. The image decoding method of claim 14, wherein when thecurrent block is a luma block and the LFNST index is 0, the MTS index isparsed.
 16. The image decoding method of claim 14, wherein when a treetype of the current block is a dual tree, the LFNST index for each of aluma block and a chroma block is parsed.
 17. The image decoding methodof claim 14, wherein the deriving the transform coefficient comprisesderiving a width and a height for a top-left region in which a lastsignificant coefficient may exist in the current block by zero-out, andwherein the width and height for the top-left region are derived beforeparsing the MTS index.
 18. The image decoding method of claim 17,wherein the last significant coefficient position is derived based onthe width and the height for the top-left region, wherein lastsignificant coefficient position information is binarized based on thewidth and the height for the top-left region.
 19. An image encodingmethod performed by an encoding apparatus, the method comprising:deriving prediction samples for a current block; deriving residualsamples for the current block based on the prediction sample; derivingtransform coefficients by applying at least one of LFNST and MTS for theresidual samples; and encoding residual information related to thetransform coefficients and at least one of an LFNST index related to anLFNST kernel and an MTS index related to an MTS kernel, wherein theLFNST index is encoded before the MTS index, and wherein the MTS indexis encoded based on a value of the LFNST index.
 20. The image encodingmethod of claim 19, wherein when the current block is a luma block andthe LFNST index is 0, the MTS index is encoded.
 21. The image encodingmethod of claim 19, wherein when a tree type of the current block is adual tree, the LFNST index for each of a luma block and a chroma blockis encoded.
 22. The image encoding method of claim 19, wherein thederiving the transform coefficient comprises deriving a width and aheight for a top-left region in which a last significant coefficient mayexist in the current block by zero-out, and wherein the width and theheight for the top-left region are derived before signaling the MTSindex.
 23. The image encoding method of claim 22, wherein the lastsignificant coefficient position is derived based on the width and theheight for the top-left region, and wherein the last significantcoefficient position information is binarized based on the width and theheight of the top-left region.
 24. A non-transitory computer-readabledigital storage medium which stores a bitstream generated by a method,the method comprising: deriving prediction samples for a current block;deriving residual samples for the current block based on the predictionsample; deriving transform coefficients by applying at least one ofLFNST and MTS for the residual samples; and encoding residualinformation related to the transform coefficients and at least one of anLFNST index related to an LFNST kernel and an MTS index related to anMTS kernel to generate the bitstream, wherein the LFNST index is encodedbefore the MTS index, and wherein the MTS index is encoded based on avalue of the LFNST index.